It sounds to me like the question is: Are you willing to marry him under the circumstances, knowing that he is happy with the way things are? Are you sure he doesn't have some gay issue, underneath everything?

What would his response be if he knew you were involved with another man?

If I had to say one way or the other, then I would say, "No, it doesn't look like things can be fixed." But you are the one who needs to deal with the reality of the circumstances. If I were "Dear Abby," then I would probably say, "Move on," since he sees nothing wrong and doesn't want counseling.