I know you're already annoyed so I hope this won't make it worse because that's not my intention, but "me" time can be really hard to find with a little one or several of them in the house.
To me, it sounds like things aren't that bad. I mean, he gets up in the night for the baby, he gets up with him and does the morning stuff.
Are you feeling that he should get home earlier from work so he can do the night time and bed time stuff too including folding laundry?
I understand being dead tired when you get home from work, trust me. I raised two kids as a single mom and there wasn't any help with anything, including finances.
Couples need to find a way to work things out and it's not always 50/50. One of my friends husbands does all the cooking and grocery shopping. He is the thrifty one and the one who plans meals. They say necessity is the mother of invention, hey....she is a terrible cook. She does not have a knack for it. Have you ever seen the show "Chopped"on the Food Network?
The baskets they get with the weirdest combinations of things to make meals out of was basically the same result after one of her shopping expeditions.
He does the cooking and she does the cleaning and putting the groceries away. She's a teacher and very organized and meticulous when it comes to that.
She does the yard work. One summer when he was away fighting wild fires, she painted the house. By herself. Well, my son helped her because he was out of school and I was at work.
They have figured out a way to divide things up. He's a firefighter and gone all fire season, sometimes for months at a time. He's a drummer in several bands and plays at church every Sunday he can. He's a busy guy. As a teacher, she's involved in all the school events and PTO, PTA, conferences, kids activities, etc.
They have found what works for them and they've been married about 25 years.
It doesn't sound to me like your husband doesn't help with the baby at all and if you need some "me" time, it kind of sounds like you have it in the evenings after your baby is in bed and your husband is still gone. Take a nice soak in the tub with lots of bubbles, light some candles, just enjoy that quiet time. So what if the laundry doesn't get folded.
The trick to laundry is to fold it and/or hang it up right when you take it out of the dryer. I never felt like it, still don't, but then it really is so much easier than having a pile of laundry somewhere. Whoever takes the stuff out of the dryer should fold it and put it away. Take turns.
If I were you, I would take every moment you have between the baby going to sleep and your husband getting home to soak in the tub, paint your nails, pamper yourself a little.
I'm trying to cheer you up and it may not sound that way, but I am. Try to communicate with your husband without "complaining". Try to have a discussion in which you acknowledge the long hours he works and the fact that he does help with the baby.
I think that might make him more open to listening to your feelings.
Just my opinion.
Best wishes.