Calm down first!

It's only two months. Your husband may already terminate the relationship. He flew to see the other party is reasonable. At least he showed respect and care to the other party. Now you need ask yourself if you can forgive him. Talk to him, make sure you understand him and he understands you first. In the meanwhile, think why you guys end up with this. Good luck!

If he wants to email out the termination email and copy that to you , so let him do it. Then if you caught him again after the termination email, you will have evidence. Make sure when you caught him again, you will have some concrete evidence.