IMO, the joking about your adultery is ridiculous. I can tell you that if I were him... YOU had better never joke about something like that. That would be a major LB and frankly NEVER something to joke about.

Your H's relationship with the OW is not really over untilo such a time is there is NC... and because he did not tell you about the email, I would have appropriate concern about that. I believe you should bring this up to him and see what he says. You should not "appreciate" him failing to be honest with you. In the face of both of you having affairs, I would suggest that there is nothing more important than honesty right now. Both of you let your character and integrity take a vacation.... it is time to reclaim that.