Even though your husband cheated on you in your marriage, it does not mean that your relationship is headed for divorce. Saving your marriage and bringing your husband to a stage where he will stop cheating will be a tough emotional road, but you might find it worthwhile in the end. If you're willing to make sacrifices and work with him through this trying time in your marriage, you could see your marriage take a turn for the better.
Confront your husband in a calm, mature manner about his cheating. Let him know upfront that you do not want the conversation to turn into an argument, and do not yell at him. Tell him that you want to work on the marriage because you want to see it last. This may be a lot for him to take in, so give him a day or two to think it over and let it sink in. If your marriage is to be saved, both of you must be on board.
Talk to your husband after he decides to work with you to save your marriage. Find ways for him to cut off all contact with his girlfriend and for him to let her know they can no longer see each other.
Discuss reasons why he began to cheat, and get to the root of the problem. You might want to seek marriage counseling to help with this process. A trained professional will be able to help you get to the root of your marriage problems and can suggest solutions to those problems.
Continue to show affection toward each other and don't act coldly toward your husband. If he genuinely loves you, he'll feel badly about what he did and will want to show you that he still cares and that he is sorry. Acknowledge his efforts to reconcile with you and work with him on these efforts. Go on dates and do things together that both of you enjoy. Try to forget about the past and forgive him for his misbehavior.