I am sorry that you have received such a blow. The first thing you need to know about an affair is that the partner who cheats is indirectly expressing a great deal of anger toward his/her spouse. Your husband 's behavior is no exception. Instead of speaking about what has angered him, your husband has resorted to enacting his anger by giving you this emotional blow.
If the marriage is going to be saved, he must be willing to stop acting and start talking about his anger and whatever else has been eating him about you and the marriage. I know that you are feeling wronged and violated by his behavior; there is no question that he betrayed you and that you have been violated. However, if you wish to save the marriage, you will need to resist the temptation to play the victim and point the finger at him for being the bad guy (yes, he behaved badly, and he did you wrong). Nevertheless, pointing the finger at him and falling into the blame game will anger him further and won't help you to solve the marital problems that led to his cheating.
Obviously your husband needs to admit that he cheated on you as a precondition for working on the marriage. He is likely reluctant to do so for fear of losing vital bodily parts. If he discovers that you aren't out to castrate or maim him, and that you are willing to take responsibility for your role in the erosion of the marriage, he should be more willing to admit that he did, in fact, cheat, as well as be more open to addressing the marital problems that led him to handle his discontent in such an inappropriate way.
So, do whatever you need to do to purge yourself of the hurt and anger over his betrayal (talk to a friend, a priest, a therapist) and then move to the next level: accept that the affair is a symptom of an ailing marriage. It takes two people to create an ailing marriage, so both of you are going to need to ask yourselves: what have I done to break the connection and what can I do to restore it. Looking into yourselves will help you avoid the counterproductive habit that most couples fall into of counterblaming, a deadly habit that will not solve your problems and will likely end you up in divorce court.
So each of you must take the first step to repairing the relationship by looking inward and taking responsibility for the disintegration of the marriage. This is a very simple program, but hard to put into practice. You may need help to get on track and stay on track. My book, by the way, can certainly help you both to learn how to talk about the problematic issues without resorting to blame fests.
My book will also show you how to take turns listening and understanding each other as well as how to resolve your issues. Good luck.