It's really difficult sometimes for people who grew up in happy, healthy households to understand just how badly years of verbal abuse and emotional abuse can fuck you up.
I grew up in such a household, with an extremely controlling father. I was basically considered an object. I was his daughter so he "owned" me. That meant he owned my time. I was expected to drop anything and everything at the last minute to cater to his every whim, from listening to three hour rants well into the wee hours of the morning about his job to painting, sanding, and tiling for his dream house and rental properties, often all weekend. I was treated as slave labor and if I had other plans, like doing homework or visiting friends, I was told I "obviously wasn't committed to the family" and I "didn't love my parents." He also owned my aspirations, dictating what extracurriculars I could participate in and putting me down constantly if I chose to spend my time on hobbies and organizations he didn't approve of. If I argued with him, it was because I didn't "value his opinion" and "thought he was an idiot" and "didn't really want to succeed." It even came down to owning my friends and bfs. Growing up, my dad was constantly bullying me into volunteering my friends for free labor on his rental properties, driving him to the airport, taking care of the cats while we're on vacation. He never gave a reasonable warning too, it was always, "L.A.Lime, I need three guys to help me move furniture tomorrow; if your friends really love you, they'll volunteer. Obviously, if they don't care about your family, they aren't your friends."
After years and years and years of being taught, from grade school up, that if you don't cater to your parents' every whim, you are a horrible person, it gets ingrained in you. To this day, if my dad yells at me, even over something really dumb, I have a crying fir for hours. I know it's irrational, but that guilt is a learned emotional response that makes me feel like shit if I don't obey my dad's every word. On top of that, if you've been taught from a young age that having your boundaries ignored is "normal," it's hard to recognize when abuse is happening.
I used to worship the ground my dad walked on and it took years or re-learning what a normal relationship looks like and lots of therapy to unlearn a lot of maladaptive behaviors from my childhood and start to undo some of the damage. It's hard, really really hard. But it can be done with time and effort. Now, I no longer let my dad walk all over me; he tries, but I have boundaries I've learned to enforce and the support of an awesome bf.
Your SO needs therapy to re-learn that it's okay to have boundaries, that emotional & verbal abuse are actually abuse, and that he has a responsibility as your husband not to let his parents' abuse translate into abuse toward you. This will be a very difficult conversation to have, because he most likely doesn't see his parents as being abusive at all; this is his norm. Try getting him to go to couple's counseling with you; a professional will be better tailored to help him see the light.