Oh ladies I am beyond heart broken

I confronted DH about the sex thing. For some reason today, out of no where, I thought "surely a man has to ejaculate at least every few weeks. In the form of sex, masturbation, wet dreams whatever"
(Sorry for this personal post!)
So I asked him tonight if he masturbates and he said no. So I explained my theory that testosterone levels would make the sperm come out one way or another. He kept denying it but I could see he was almost embarrassed. So I kept on at it.
He eventually admitted to doing it

he said not often. Now let me just say even when we did have sex, once a week was a huge achievement. It was usually once every second week. So I ask how often he masturbates. He says not more than once a week! I said that for 3 months I have been begging him to be intimate with me in ANY form and he's always said he's not in the mood cos he's stressed and tired. Now I find out he's pleasuring himself once a week so its clearly more about just not wanting to be near me intimately. I am hurting SO much. I feel so ugly, unattractive and now clearly useless too. I can't believe he's been doing that all along while telling me he has no sex drive from stress.
He must know I'm hurting...but he just rolled over and went to sleep. When I asked him if ignoring me will make the problem disappear, he said "I have to sleep-I have work tomorrow so just leave me to sleep"
So now I must lie here thinking of what I've just found out and feel even more pathetic? Oh my goodness my heart is so sore

what kind of relationship is this