I'm a guy in a relationship much like yours. My fiancee's girlfriend is lesbian and though I have known her and liked her for longer than I've been going with my fiancee, she has no sexual desire for me. She always made it clear that there would be no sex between us no matter how close and affectionate we get, which is pretty close since she often sleeps with us.
It's up to him to understand and accept you for who you are and to decide to love you even if he wishes things were different. Nothing's perfect: you don't always get what you want. I think you have to accept limitations in any relationship, this is just one. I don't see anything to break up over.