Exhibit 8.1

July 13, 2018

Boards of Directors

Banks of the Chesapeake, M.H.C.

Chesapeake Bank of Maryland

CBM Bancorp, Inc.

2001 East Joppa Road

Baltimore, Maryland 21234

Ladies and Gentlemen:

You have requested this firm’s opinion regarding the material Federal and State of Maryland income tax consequences that will result from the conversion of Banks of the Chesapeake, M.H.C., a federal mutual holding company (the “Mutual Holding Company”) into the capital stock form of organization (the “Conversion”), pursuant to the Plan of Conversion and Reorganization of Banks of the Chesapeake. M.H.C., dated May 23, 2018 (the “Plan”), and the integrated transactions described below.

In connection with our opinion, we have made such investigations as we have deemed relevant or necessary for the purpose of this opinion. In our examination, we have assumed the authenticity of original documents, the accuracy of copies and the genuineness of signatures. We have further assumed the absence of adverse facts not apparent from the face of the instruments and documents we examined and we have relied upon the accuracy of the factual matters set forth in the Plan and the Registration Statement filed by CBM Bancorp, Inc., a Maryland stock corporation (the “Holding Company”), with the Securities and Exchange Commission (“SEC”) under the Securities Act of 1933, as amended, and the Application for Conversion on Form AC and Application on Form H-(e)1 filed by the Mutual Holding Company with the Board of Governors of the Federal Reserve System (the “Federal Reserve”). In addition, we are relying on letters from Feldman Financial Advisors, Inc. to you, dated June 1, 2018, stating its belief as to certain valuation matters described below. Capitalized terms used but not defined herein shall have the same meaning as set forth in the Plan. Furthermore, we assume that each of the parties to the Conversion will comply with all reporting obligations with respect to the Conversion required under the Internal Revenue Code of 1986, as amended (the “Code”), and the regulations thereunder (the “Treasury Regulations”).

Our Federal tax opinion is based upon the existing provisions of the Code, and the Treasury Regulations, and upon current Internal Revenue Service (“IRS”) published rulings and existing court decisions, any of which could be changed at any time. Any such changes may be retroactive and could significantly modify the statements and opinions expressed herein. Our Federal tax opinion is not binding upon the IRS or any other taxing authority. Similarly, any change in the facts and assumptions stated below, upon which this opinion is based, could modify the conclusions herein. This opinion is as of the date hereof, and we disclaim any obligation to advise you of any change in any matter considered herein after the date hereof.

We opine only as to the matters we expressly set forth herein, and no opinions should be inferred as to any other matters or as to the tax treatment of the transactions that we do not specifically address. We express no opinion as to other federal laws and regulations, of any others state laws or regulations, or as to laws and regulations of other jurisdictions, or as to factual or legal matters other than as set forth herein.

For purposes of this opinion, we are relying on the representations as to factual matters provided to us by the Mutual Holding Company, Chesapeake Bank of Maryland (the “Bank”) and the Holding Company, as set forth in the certificates for each of those aforementioned entities and signed by an authorized officer of each of the aforementioned entities, incorporated herein by reference.

Description of Proposed Transactions

Based upon our review of the documents described above, and in reliance upon such documents, we understand that the relevant facts are as follows. The Bank became the wholly owned subsidiary of the Mutual Holding Company in 1998. The owners of the Mutual Holding Company are the depositors of the Bank, who are entitled upon the complete liquidation of the Mutual Holding Company to any liquidation proceeds after the payment of creditors.

The Boards of Directors of the Mutual Holding Company, the Holding Company and the Bank have adopted the Plan providing for the Conversion of the Mutual Holding Company from a federally chartered mutual holding company to the capital stock form of organization. As part of the Conversion, the Holding Company will succeed to all the rights and obligations of the Mutual Holding Company, and will offer shares of Holding Company Common Stock to depositors and certain borrowers and members of the general public in the Offering.

Pursuant to the Plan, the Conversion will be effected as follows and in such order as is necessary to consummate the Conversion:

Following the Conversion, a Liquidation Account also will be maintained by the Holding Company for the benefit of Eligible Account Holders and Supplemental Eligible Account Holders who continue to maintain their deposit accounts with the Bank. Pursuant to Section 19 of the Plan, the Liquidation Account will be established by the Holding Company at the time of the Conversion in an amount equal to the Mutual Holding Company’s total stockholders’ equity as reflected in the latest statement of financial condition contained in the final Prospectus used in the Conversion, plus the value of

the net assets of the Mutual Holding Company as reflected in the latest statement of financial condition of the Mutual Holding Company prior to the effective date of the Conversion. Following the Conversion, the Liquidation Account will be maintained for the benefit of the Eligible Account Holders and Supplemental Eligible Account Holders who continue to maintain their Deposit Accounts at the Bank. Each Eligible Account Holder and Supplemental Eligible Account Holder shall, with respect to his or her Deposit Account, hold a related inchoate interest in a portion of the Liquidation Account balance in relation to his or her Deposit Account balance at the Eligibility Record Date or Supplemental Eligibility Record Date, respectively, or to such balance as it may be subsequently reduced, as hereinafter provided. The Holding Company shall cause the Bank to establish and maintain the Bank Liquidation Account for the Eligible Account Holders and Supplemental Eligible Account Holders who continue to maintain their Deposit Accounts at the Bank. The terms of the Liquidation Account and Bank Liquidation Account are set forth in Section 19 of the Plan.

As a result of the Conversion and Offering, the Holding Company will be a publicly-held corporation, will register the Holding Company Common Stock under Section 12(b) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and will become subject to the rules and regulations thereunder and file periodic reports and proxy statements with the SEC. The Bank will become a wholly owned subsidiary of the Holding Company and will continue to carry on its business and activities as conducted immediately prior to the Conversion.

The stockholders of the Holding Company will be those persons who purchase shares of Holding Company Common Stock in the Offering. Nontransferable rights to subscribe for the Holding Company Common Stock have been granted, in order of priority, to Eligible Account Holders, the Bank’s tax-qualified employee plans (“Employee Plans”), Supplemental Eligible Account Holders, and certain other depositors of the Bank as of the Voting Record Date (“Other Members”). Subscription rights are nontransferable. The Holding Company will also offer shares of Holding Company Common Stock not subscribed for in the Subscription Offering, if any, for sale in a Community Offering or Syndicated Community Offering to certain members of the general public, and if shares remain after the subscription and community offerings, shares may be offered, at the sole discretion of the Holding Company, to members of the general public in a Syndicated Community Offering.

Federal Tax Opinions

With respect to items 5 and 7, above, Jones Walker LLP noted that the subscription rights will be granted at no cost to the recipients, are legally non-transferable and of short duration, and will provide the recipient with the right only to purchase shares of common stock at the same price to be paid by members of the general public in any community offering. The firm further noted that Feldman Financial Advisors, Inc. has issued a letter that the subscription rights have no ascertainable fair market value. The firm also noted that the Internal Revenue Service has not in the past concluded that subscription rights have value. Based on the foregoing, Jones Walker LLP believes that it is more likely than not that the nontransferable subscription rights to purchase shares of common stock have no value. However, the issue of whether or not the nontransferable subscription rights have value is based on all the facts and circumstances. If the subscription rights are subsequently found to have an economic value, income may be recognized by various recipients of the subscription rights (in certain cases, whether or not the rights are exercised) and the Holding Company and/or the Bank may be subject to tax on the distribution of the subscription rights.

Our opinion under paragraph 6 above is based on the position that the benefit provided by the Bank Liquidation Account supporting the payment of the Liquidation Account in the event the Holding Company lacks sufficient net assets has a fair market value of zero. We understand that: (i) no holder of an interest in a liquidation account has ever received payment attributable to such interest in a liquidation account; (ii) the interests in the Liquidation Account and Bank Liquidation Account are not transferable; (iii) the amounts due under the Liquidation Account with respect to each Eligible Account Holder and

Supplemental Eligible Account Holder will be reduced as their deposits in the Bank are reduced as described in the Plan; and (iv) the Bank Liquidation Account payment obligation arises only if the Holding Company lacks sufficient net assets to fund the Liquidation Account.

In addition, we are relying on a letter from Feldman Financial Advisors, Inc. to you stating its belief that the benefit provided by the Bank Liquidation Account supporting the payment of the Liquidation Account in the event the Holding Company lacks sufficient net assets does not have any economic value at the time of the Conversion. Based on the foregoing, we believe it is more likely than not that such rights in the Bank Liquidation Account have no value.

If such rights in the Bank Liquidation Account are subsequently found to have an economic value, income may be recognized by each Eligible Account Holder and Supplemental Eligible Account Holder in the amount of the fair market value of their interest in the Bank Liquidation Account as of the effective date of the Conversion.

Discussion of State of Maryland Income Tax Matters

Title 10 of the Annotated Code of Maryland outlines the provisions for income tax in the State of Maryland. Income tax for individuals and corporations is addressed in Subtitle 2 and Subtitle 3 of the Annotated Code of Maryland, respectively. The Maryland modified income of a corporation is the corporation’s federal taxable income for the taxable year as determined under the Internal Revenue Code and as adjusted under Title 10, Subtitle 3, Part II of the Annotated Code of Maryland. In general terms, a corporate reorganization is a tax-free transaction under federal law if the consideration for the acquisition consists primarily of stock or securities of the acquiring corporation or its parent. In most cases, the gain or loss recognized on a reorganization for Maryland tax purposes will be the same as the gain or loss recognized for federal tax purposes because Maryland uses federal taxable income as the starting point for the computation of its tax base and there is no provision of Maryland law that modifies the federal recognition or non-recognition rules applicable to reorganizations.

In that subscription rights will be granted at no cost to the recipients and provide the recipients with the right to only purchase shares of common stock at the same price to be paid by members of the general public in any Community Offering, there is no ascertainable value and, therefore, no Maryland individual income tax consequence to the granting of the subscription rights. Taxable income could only be computed if there is a value to the subscription right when it is granted or if the subscription right allowed the grantee to purchase the common stock at a value below the price members of the general public would have to pay to purchase the same common stock. Maryland individual income tax starts with federal adjusted gross income and no modification is provided for receipt of subscriptions rights with no ascertainable value.

State of Maryland Tax Opinions

Based upon our review of the agreements and documents mentioned above, additional representations and information provided, and our federal income tax opinion, it is our opinion that with respect to Maryland income tax:

1. To the extent the merger of Banks of the Chesapeake, M.H.C. with and into CBM Bancorp, Inc. qualifies as a tax-free reorganization within the meaning of Section 368(a)(1)(A) of the Internal Revenue Code, then such merger will not result in any income tax liabilities under Title 10 of the Annotated Code

of Maryland. Our Federal income tax opinion provides that it is more likely than not that none of the entities involved will recognize gain or loss upon the receipt of assets or the assumption of liabilities in exchange for shares of stock or the constructive distribution of any such stock or an interest in a liquidation account or the constructive distribution of such liquidation account. For Maryland income tax purposes, the Eligible Account Holders, Supplemental Eligible Account Holders and Other Members will follow the Federal non-recognition treatment.

2. For Maryland income tax purposes, Banks of the Chesapeake, M.H.C. will not recognize any gain or loss on the transfer of the assets of Banks of the Chesapeake, M.H.C. to CBM Bancorp and the assumption by CBM Bancorp of Banks of the Chesapeake, M.H.C.’s liabilities, if any, in the Merger, pursuant to which Eligible Account Holders and Supplemental Eligible Account Holders will receive interests in the Liquidation Account of the Holding Company in constructive exchange for their liquidation interests in the Mutual Holding Company.

3. For Maryland income tax purposes, no gain or loss will be recognized by CBM Bancorp on the receipt of money in exchange for CBM Bancorp common stock sold in the offering.

4. No Maryland income tax will be imposed on account holders of the Bank upon the constructive distribution to them of any rights in the Chesapeake Bank of Maryland liquidation account.

5. No Maryland income tax will be imposed on Eligible Account Holders, Supplemental Eligible Account Holders and Other Members upon the issuance to them of Subscription Rights.

6. With respect to Maryland income tax, the holding period and tax basis of any stock involved in the proposed Conversion will be the same as for Federal tax purposes.

In providing our Maryland tax opinion, we have considered the provisions of Maryland tax law and the interplay of the Internal Revenue Code of 1986, as amended, Maryland tax regulations, judicial decisions and Maryland Comptroller rulings, to date. A change in the authorities upon which our opinion is based could affect our conclusions. Moreover, there can be no assurances that our opinion expressed herein, if challenged, will be accepted by the State of Maryland. We have assumed the authenticity of original documents, the accuracy of copies and the genuineness of signatures. We have further assumed the absence of adverse facts not apparent from the face of the instruments and documents we examined.

Since this letter is provided in advance of the closing of the Conversion, we have assumed that such transactions will be consummated. Any change to the Plan could cause us to modify the opinions expressed herein.

We have not been asked to, and we do not, render any opinion with respect to any matters other than those expressly set forth above.

CONSENT

We hereby consent to the filing of the opinion as an exhibit to Banks of the Chesapeake, M.H.C.’s Application for Conversion filed with the Federal Reserve and to CBM Bancorp, Inc.’s Registration Statement on Form S-1 as filed with the SEC. We also consent to the references to our firm in the Prospectus contained in the Application for Conversion and Form S-1 under the captions “The Conversion and Offering—Material Income Tax Consequences” and “Legal and Tax Matters.”

Very truly yours,

/s/ Jones Walker LLP

Jones Walker LLP