There are several of us here, when the AP was same-sex. I'm one of the "older" ones on here.
My ex's life was only blown open because he ticked off one of them. I think if that man hadn't tracked me down and told me, I'd still be married. Ex cheating when he travelled, just like you...it was so easily hidden. My ex had been doing it for YEARS when d-day hit.
We did try to R for close to 9 months. At that point, married for 15 years, together for 17 and I was a SAHM with 2 children.
I desperately wanted to believe my ex was bi-curious, or even bi-sexual. But, I did enough reading to learn it is a very, very small minority of men with "gay thoughts" that don't eventually act on them. Some, yes, do survive this and go on to a good marriage. There are support groups out there for "open marriages" and marriages where one spouse is gay but chooses to stay in a hetero relationship. But, I contend that the man has to be VERY emotionally strong and communicative for the marriage to survive. You've got to be able to openly and honestly talk with each other about some very painful topics.
There are likely parts of him that he needs to explore. You don't wake up one day and decide to have sex with a man. My H had a gay experience in high school (never told me!), then married me at 22. The best I can tell, he was faithful for a few years.
What he told me was that when he met me, "He thought his question had been answered" since he fell in love with me. Then, later, he felt he deserved to cheat on me to "figure this out". He treated me terribly during those years. And, yes, we were still having an active sex life, although now that I've been with heterosexual men...the sex is different with a hetero guy.
Get tested. Now. There is likely more to the story. Get yourself into therapy. A strong IC who isn't afraid to discuss gay issues and can support you on YOUR journey through this. Your H is likely on a journey trying to figure out who he is. It is a hard journey to go on. He doesn't want to hurt you, yet he was driven to do this. You mention an email account? I'm guessing you are just beginning to discover what he has been hiding.
It was hard for me to listen to people say, "This is just the beginning. There is probably more. There are few true bi-sexuals, he is likely gay. Protect yourself and your future. Get to a lawyer NOW. " Trust us. Just do the hard things while things are playing out...You don't have to divorce him if things settle down and he does the hard work. But, you have a responsibility to protect yourself. He didn't protect you...you have to protect yourself. My ex was also drinking heavily during this time.
I have doubts that a pastor is really going to be able to help him. Being forgiven is wonderful, but that isn't going to answer the question of "why?". You don't want to "rug-sweep" this and then he cheat again in a year...or few years...because he didn't address the reasons and come to term with the answers.
For me, it was all true...he is 95% gay. I say 95% because he would still have sex with me if I gave him the opportunity. But, I'm the only woman he has ever been with. He has been with many, many men. He is now in an openly gay relationship of 2.5 years. Our kids know. I moved forward, got myself into grad school, moved my kids and am happy and dating. I've worked hard at healing after that nightmare. Regardless of what you choose to do, we will be here to support you. You will survive...and thrive...regardless of what happens.
Make sure you are eating, drinking and have some supportive friends you can talk to.