I'm not an infj (intp f), but am an atheist who married into a Filipino catholic family too, and I am currently living with them because spouse doesn't want to leave his newly single mother (divorce) without a guy in the house. No kids yet, so I don't have your level of stress, but I can empathize.

I constantly hear passive aggressive comments on my parenting, appearance, cooking, etc.

Haha, oh dear, it is a flip thing. Sorry for laughing, I used to think it was weird to constantly hear weight comments about me from my chubby in-laws. And it can be so bitter too. Its not about you, the culture can be very negative, with the running joke being that parents say to their kids, "so you think you're somebody." It isn't personal and it is a form of hazing that you get in Asian cultures (I'm also korean-american.) Daughter-in-laws get alot of flack.

How I navigate this:
(1) I go to church once in awhile.

(2) I had a catholic wedding, essentially promising to raise the kids catholic. I figure that I'll raise the kids to be independent minded and make their own decisions. Not saying this is something to do, especially if you have any qualms about your common-law spouse

3) I do all the small silly things asked of me. I ignore things said about me because it says more about their insecurities than who I am as a person. Everyone has their own style of doing things, and criticisms on that level are ignored or some some small/miniscule concession is made. Legit criticisms I make an effort to improve upon, and it is appreciated. You may need to announce that you made the change though.

4) Everyone has a temper. If ugliness needs to come out before something productive is said, let him say his piece without interrupting him. He's probably under stress too, and what he will have a kernel of truth. Respond to that kernel. Keep your cool and don't give into the temptation to join in the ugliness. If he needs time to recover, give it to him, but go back to the topic. Tell him you will give him his space, but you need a resolution, so you won't and can't back off completely.

Also have solutions ready, not just the problems. Don't back him into a corner between his parents and you without a way out aka solutions that protects you/him/parents.

Every day I drink whatever alcohol I can get my hands on or if weed is around, sneak away with that for some relief.

Not a good sign. You know it, and your spouse is probably aware of this. Be upfront about this if you trust him.

Best of luck and lots of internet hugs.