The "they don't mean it" excuse is often trotted out by outsiders (and worse, many insiders too) who are confronted by parents abusing their (adult) children. It's minimisation. It's disrespectful and hurtful at best, at worst it means that they condone, are complicit to, and encourage the ongoing abuse of the child.
But actually, it doesn't matter whether abusive parents mean to be abusive or not. If they've been told that their behaviour is hurting the adult child, and they choose to not apologise and change their behaviour, it is completely reasonable that the adult child institutes boundaries that protect her/him from further harm. Including low contact or no contact.
The same goes, then, for people who want to minimise the harm that has been done or is still being done to you by an abusive person. Boundaries are needed for these people as well.
Boundaries are not to punish, they are to protect. An example is when I cut my father off, when I was 40. He refused to pay my mother her share of the retirement they had built up together (because he took advantage of a law, which has since been overturned because of this kind of behaviour by men). He left her in scrabbling poverty, compounded by severe ill health. I could not accept this heinous act. It was the last straw in a lifetime of trying to have an relationship with an indecent person who treated other people horrendously. I wrote my father, warning him that this was not and never would be acceptable to me. I gave him a chance to reconsider. He would not.
When he realised that I had cut him off, he sent some Flying Monkey friends and relatives, even one of MY friends, to plead his case:
"He's your father".
"You have to forgive him".
"You never know what goes on in a marriage".
"He looked after you financially growing up, you owe him".
"He misses you and is sad."
"You'll regret it when you're older."
I told each one of them, "My decision was not made lightly. It was forced by my father and made in great sorrow and with deep pain. If you do not respect my decision, I will not see you again either."
None of them ever talked about it again. We have had fine, loving, mutually respectful relationships that continue to this day or until their deaths.
That's a boundary. Protection, not punishment.
OP, determine what you need to protect yourself, and put in that boundary with your H, whatever it looks like.