My husband has a problem that I did not know about until after we were married but has evidently been going on for years. For one thing, he is addicted to pornography. When I enter the room with him ...
Others might say that his obsession isn't hurting anyone if he's able to function in the world and as a husband and so he should be left alone. However, you're telling us he sneaks and that is definitely harmful to your marriage (also harmful is doing it in spite of your feelings about it). He should realize that it is time to get help or suffer the consequences.
It's evident that your husband has had these behaviors for a long time. Anyone who deals with addiction (like gambling or smoking) knows you probably can't just stop doing whatever it is you're doing. If his behaviors are ingrained, it will take a lot of commitment and expert help in the form of a therapist who is experienced in addiction issues. I would guess that there's really nothing you can do and asking him to stop is like asking birds not to fly; that doesn't mean you shouldn't support him and help him any way you can. Right now, I think the best you can do is to tell him your marriage depends on his starting therapy, but you must then be prepared to leave him if he doesn't follow through (if you don't, he knows you're not serious about the threat and you become the dreaded "enabler" - just as women who are beaten by their husbands and then don't press charges). He must understand that continuation of this habit will eventually kill your feelings for him.