I'd be diggin out my employment policy manual/sylabus/pamphlet or what have you, and reading up on the rules and regulations regarding confidentiality of what is heard or seen while on duty. In my line of work, a breach of confidence can result in a fine as great as $250,000.00 dollars and several years in jail.
Hmmmmmm.... which is worse, ruining your whole life, or sitting on a secret. The one person you CAN discuss it with without breaking confidentiality is the woman cheating. She knows she cheated, she suspects you heard. If you "NEED" to unload your secret, I would unload it directly on her and keep your wife out of it. If you feel put out, TELL her you do NOT appreciate being put in such a position. I would not give her any ultimatums or directives either. Just tell her you know... let her sweat bullets instead of you.