I see your boyfriend as somebody who's on an enormous quest to find "The One", and he searches everywhere he can. It appears that he realizes that you two are very close and that you never did anything wrong to deserve this, but he wants to continue his search anyway. Somehow, deep within his subconscious he is searching for a certain type of woman that he can't quite define; it's as if her shadow is lurking in the far reaches of a hidden place, but chances are she's nothing more than a distant memory of a celebrity such as Cindy Crawford or Kate Moss.
I suspect that he's already in a relationship with the woman he plans to visit. They have a long distance relationship by email and over their cell phones, and they're planning to treat his visit as their honeymoon.
You have every right to know how bad your situation is. Tonight send him an email that looks like this: "Please email me the password to your email account right now. I do not want to discuss the reason why I want it." He'll instantly know what's up, and he will delete his entire inbox before he gives it to you. When you open his email account, press on the "Trash" button, or the "Deleted Files" button, or whatever they call it.
Certain email carriers allow their subscribers to permanently delete trash so that it can not be retrieved. If you have $100 to spend, take his computer to a repair shop and tell the technician that you have deleted email on your hard drive that you need to retrieve (for a project at work). They can retrieve anything that has been deleted on his computer.
Chances are your boyfriend won't relinquish his password or his computer. Instead he'll break up with you because it's easier than dealing with you after you've read his deleted email. He'll accuse you of being jealous and unreasonable. He'll ask you why you want it a million times as if he's 10 years old. Be prepared for all of it. Just say that you don't want to discuss it, and you simply want his password and his computer. If he breaks up with you, than say that you don't need to see his computer anymore, but that you never, ever want to hear from him again under any circumstances. Not on Christmas, not 3 weeks from now, not a year from now. Never, ever.
There was a movie that was sort of like this called "Little Black Book", starring Brittany Murphy. It's a romantic comedy, but in the end she left her boyfriend because he was still attached to one of his ex girlfriends.