I agree that once you confront him, he will first deny it, and then start hiding it. So you should be prepared for this. You have two choices... you can learn to accept it and stay in the marriage, or you can move on. But you will never, ever be able to fix it. He has to do this all by himself, and this could take years.
Hmmmm... I just noticed how negative this sounded. So, let me also add that I chose to stay in the marriage. It took my husband about 22 years to find sobriety. This kind of life is not for everyone.