To me, I could not -- and would not -- ignore the gorilla in the room, and I wasn't going to continue to allow my family to be bathed in deceit from my wife. Although I initially confronted her about her affair, and exposed it to her parents and our adult daughters, she continued to lie to all of them for another month or so, even telling them "Puppy is crazy, there's nothing going on -- we're just friends." I calmly but firmly re-confronted my wife, let her know that I wouldn't tolerate having my own reputation run down when EVERYTHING I'D BEEN SAYING WAS THE GOD'S-HONEST TRUTH, and that she either told her parents and our adult children the truth, or I would, and I would show them my evidence.
I also told her she had 5 minutes to respond.
She told them the truth.
I don't think you can control their adultery, but you can certainly insist on the truth, at least when they're speaking to you. I think it's an important boundary. So whether or not you want to confront your H or not, I would at LEAST, the next time he says something you KNOW to be a lie, put your hand up in the "STOP" position and say:
"Please stop. We both know that you're lying to me right now, and it's incredibly disrespectful to me, to our marriage, and to our family. I know all about you and _______ . If you want to break your marriage vows, that's your decision, but I still not stand here and be lied to. I think I deserve at least that much, don't you?"