You each married each other - not your parents.
Your focus is all wrong.
You entered a "forever team" when you got married - not an each of you is "perfect", but the "you need to face all things as a team and work them out as a team."
No absolute rights and wrongs - but you need to grow up and work it out as a couple.
He doesn't like your parents, you don't like his, but you are less stressed than him.
He is stressed by your parents if he's flinging ultimatums. Or he's laying the groundwork for blame, if he's looking to get out of the marriage.
Assuming he's not having an affair or keeping a back pocket reason to divorce, just why is this such a problem?
Are your parents round every week? How much do they intrude?
Have you discussed what actually ticks him off about your parents and their comments?
Why don't you tell your parents politely to put a cork in it and not to insult your husband? Or are you hiding he's not a nice person?
I have a very anger and bitter MIL, ever since her husband walked out 30 years ago (affair) and for various other reasons.
Quite taken aback when her and SIL were so rude and disrespectful, about something unimportant, that wasn't quite connected to me, about 10 years ago.
My husband rarely gets angry. He's a very calm peron. But on this occasion, he bellowed with rage. Wasn't expecting the attack or counter-attack.
They shut up immediately. Never loved my husband more.
You always want your partner to have your back.
So if you're planning lifelong with your husband - don't sit on the fence - put down boundaries protecting your husband. Unless he's a jerk.
And go see your parents without him - but he needs to know you have his back.