What do you call a man who has a live-in girlfriend but still wants to sleep with his female friend?

The man in question has a live-in girlfriend but still buys me gifts, flowers, takes me out on dates, gives me just about anything I want. I told him that I couldn't accept gifts from him because he's in another relationship and that wouldn't be right but he still buys me stuff (in which I eventually throw away). We used to sleep together before he hooked up with his current girlfriend but after that, I told him that I will no longer be sleeping with him anymore because he has a girlfriend. He says that he has feelings for me but won't say what they are. I'm pretty sure that the "live-in" girlfriend knows about him messing around but won't do anything about it (like, BREAK UP WITH HIM AND MOVE OUT); and I'm also pretty sure that I am not the only one he has been sleeping with (because what man rides around with condoms kept in the car -oops, I mean, MINIVAN aka the HUMPMOBILE by even HIS OWN SON, at ALL times); but his girlfriend decides to stay with him anyway. This is all confusing to me. He's always there for me (ex.: keeps in touch with me, takes me to wherever I want to go, gives me pricey, expensive gifts, etc.) but I don't trust him. Even though it has been months since I slept with him, he is still buying me stuff and taking me places. He has tried unsuccessfully to get me to sleep with him but I just can't go through that heartache again. So, what I want to know is, what do you do with someone who is constantly sending you MIXED SIGNALS? Can anyone give me an answer to this mystery?