This sounds like a character trait and the probability is that he will continue to have that trait. It is possible that you can maintain the relation, but again the likelihood is the trait will remain. If you can accept this then there is a greater chance of maintaining the relation. Chances would be greatly improved if the both of you were to engage in couples therapy. You can find a good therapist at http://www.aamft.org/. Best of luck
If you require further clarification or more information, feel free to ask!
You had not mentioned the alcohol and that lessens any chance of reconciliation as does his fixation that you had an affair, Unfortunately he does not t seem disposed to modifying his belief which does not bode well for a reconciliation. As you well know it takes two to change and that does not seem to be the case. This will probably occur in all future relations as it is a character trait which he does not see as a problem,