Before proceeding with any action, you will want to verify that the cheating is occurring, directly with your husband. Also, you will want to let your husband know that this cheating hurts you deeply and hurts your marriage and that you would like him to stop cheating, assuming that that is what you want him to do.
Realize that you cannot force him to stop cheating, so at that point, assuming that he has admitted that it is happening, and you have asked him to stop, it is his choice. He can say he won't stop, say he will stop, or say one thing and do another, or any combination of those responses.
Now, it is your turn to make a decision. Is this something that you can live with, in your marriage? I'm not suggesting this, just pointing out that it is your decision. Realize that even if he stops, it is easier for him to cheat again, once he has already cheated. If this is not something that you can live with, you need to let him know that, and follow through. In other words, if you tell him that you cannot remain married to him if he cheats, then, well, you have your answer, and what you have decided for yourself.
Deborah is #1 Jazz Singer, as well as a lifelong musician, songwriter, and sound engineer. She is also a writer who pursues a love of positive psychology. Download the "Boost Your Energy" ebook (absolutely free!).