To be blunt, he doesn't sound as though he's going to throw in the image he is giving to the rest of the world (straight guy with a girlfriend). He is probably flattered by your attention, and he sounds as though he probably doesn't see you as just a friend(!) But as I said, I doubt he's going to come out and let anyone else know that anytime soon.
So... you have two choices as I see it:
a. You carry on as things are; sleeping together and spending time together in private but accept that it's not going to be more than that.
b. Protect yourself emotionally and tell him it's not happening any more and move on.
I don't know which I'd suggest - both have advantages and disadvantages (as you can probably see).
Either way, good luck!