I think you might both benefit from counselling. Individually and (if there is any chance of you staying together) as a couple.
My ex turned out to be gay. He denied it and denied it for a very long time. Categoric 'no' when asked directly. We did have sex, but I know now that it wasn't what it's like in a 'normal', loving relationship with mutual attraction. Many other people in my situation report little or no sex in their relationships.
If there are strong religious factors, that can be a big part of being gay in denial.
I'm not saying your H is gay. Only he knows that. But some people are able to push their sexuality away for many years before they are able to confront it.
And if he's not gay, then there is something else going on but it's not fair to you or your relationship to live like this. Sooner or later, the feelings of rejection will start to seriously affect you and your self-esteem. (Speaking from experience there, doesn't matter what the reason behind it is).
Counselling for yourself could really help you to work out what you want for yourself, and how to put yourself and your own needs first.
Best of luck to you. It is very, very difficult to take a break when you still love your partner. For what it's worth, two years on from separating from my gay ex, I'm in a really lovely relationship with a man who genuinely finds me attractive - both physically and emotionally. And it's a complete revelation. You deserve the same.