Being part of an influential Washington couple means sometimes making sure your spouse’s job doesn’t pose a conflict of interest, as in the case of the SEC’s latest nominee.

Allison Lee, a former Securities and Exchange Commission lawyer tapped for a Democratic seat on the SEC, is married to Jay Brown, a member of the Public Company Accounting Oversight Board. The SEC oversees the work of the audit regulator, selecting its board, approving its budget, and vetting any changes to...