Let me start by saying that anything I say is just my opinion, and that situations are so unique to those involved that it's hard to offer any truly useful advice from afar.
But as a tg/cd who's been married for a long time to a woman who has been wonderfully accepting and supportive, I can say without hesitation that had I not been upfront about it from day one it would have been a drastically different story. Also, had I ever strayed physically, she would have been out the door; a large part of the reason my wife has always been so supportive is precisely because she never felt she had to worry that I'd want to go out and be with a man. So while I think it's great that you're seeking to understand your husband's cross dressing, the fact that he has been so deceptive makes it so much more complicated. Fear of negative reaction is no excuse for deceiving a spouse, and there is no good excuse for infidelity in any form. So it really comes down to two things for me: do you want the marriage to continue badly enough to forgive what he's done already, and do you believe that he will stop the lies and betrayals if you do forgive? If he cross dresses for its own sake and not just as an aspect of sleeping with men, then odds are he won't stop and you'll have to be willing to accept that with him.
I wish you the best whatever you decide to do, and it breaks my heart to hear what he has put you through, but I would like to say for the record that most cd/tg are good, kind, loving people who wouldn't dream of hurting those they live in such a way--you don't seem the type anyway, but please don't let this pain taint your view of all of us. 😊
Best of luck sweetie, and I'd love to hear how it all works out once you work through it all.