At least he is not watching pornography that you know of, but I also see this situation as a dead end. Limited masturbation may be okay for singles, but with a live-in arrangement, he should be active in the real world and not get off with a fantasy.
It's not 'morally wrong' to masturbate - it's the most common sexual activity for humans, more than intercourse. I doubt you would ever find a guy who doesn't masturbate at ALL, unless he just has an extremely low sex drive, and I doubt you'd want that. Masturbation does not mean there's anything wrong with your relationship, usually it just means he has a very high sex drive & wants more frequent sexual activity than your times together provide. I will agree that generally, looking at porn is not a good thing. I think maybe he needs to tone it down a bit out of respect for you, but asking him to give up masturbation entirely is not realistic & in fact, I don't think you have a right to demand that. Likewise, I don't think a man should tell his wife or GF she shouldn't masturbate - in fact, women who do are usually more satisfied with their own sex lives & often better in bed because they know what they like & what turns them on & if they're open about it with their guy, it will lead to better sex for both partners.
Many women do not understand that for guys, masturbation does not REPLACE sex with their wife or GF, it's just an additional thing many enjoy, a quick way to get off without worrying about satisfying someone else or worrying about their own 'performance'. Most guys would tell you that sex with their wife or GF is better than masturbation, but that doesn't mean one should preclude the other. For example, I might say a juicy steak at a great steak house beats a hamburger any day, but there are time when you're just in the mood for a good burger, it's quick, tastes good & satisfies your hunger. And of course, there may be times when he's in the mood & you're not, or maybe you're not available at that moment, and masturbation is a safe, healthy practice & I think you'd agree, much better than cheating with another woman.
These are just my thought about it - it's possible you two have issues that need to be worked out that go beyond what I've expressed here...