He is gay.
I once had a boyfriend/fiancé that had a similar perspective. He surrounded himself by men, and in all pictures he is the only one hugging one or several men. Literally there is not one single picture of him with women that were not related to him, and all pictures are of him hugging other men.
Anyway, we were intimate, but he never climaxed. He was in a hurry to get engaged with me and introduced me to his family. His family was way too happy of him having a girlfriend and showered me with gifts and attention. He introduced ,e to his friends and they all would chuckle and say, but you are gay! Or yeah right! Etc. I asked him why people said that and he had a similar response as your husband's, not saying he was gay, but deflecting the question. Either you are or you are not, or you are bi, but he never accepted it but everyone else knew. One time we were checking into a hotel and he was so excited that a friend of his saw him checking to the hotel with me, he said that it would help dissipate the gay rumors. Anyway, it seem to me that he was overly prepcupied by proving that he was not gay. After we got engaged (he proposed) and I started making plans, then out of the blue and without any explanation he said that "he couldn't do it". And that was that. He is now 32, unmarried and with a guy touchy touchy entourage and people telling him to get out of the closet once and for all.
Elton John was married before he came out. I had a friend in college with a beautiful gf that came out after they broke up. In fact, I believe it was the gf that told him to seek theraphy and sort his sexuality out.
So it is more common that you think, but a lot of people have trouble coming out and maintain a heterosexual facade so not to hurt their families or face stigma.