It's not recommended, but it is legal. Some practices can not afford to have a separate coding and billing department. Naturally there's a possible conflict of interest. Coding is trying to make sure services and procedures are billed correctly following all guidelines and rules. Some service edits, contract matters, global periods, coding guidelines etc. can make full reimbursement of the fees indicated by the provider impossible. Billing is trying to collect the fees for services and procedures in an efficient and timely manner.
If handled in an ethical manner, it shouldn't be a problem having a single supervisor. Hopefully that supervisor will be knowledgeable about both billing and coding practices and applications.