Underappreciated

I'm a stay at home parent to a now 3 month old daughter. My fiance works 5-6 days a week usually getting around 40-45 hours a week. He provides all the income for our home which I appreciate so much because that means I can take care of our daughter and make sure she's taken care of properly to my standards, which I can't guarantee with a babysitter or daycare. That being said, he actually holds our daughter maybe once or twice a week, and I have to ask him to hold her so I can get things done, and usually he ends up putting her on her play mat or boppy within a few minutes. I try so hard to make sure our daughter is happy and healthy, while also making sure my fiance gets up for work in time and has everything he needs before he leaves. While I do this, he also expects me to do most of the household management, like cooking, laundry, cleaning up (mostly his messes) and all I ask is that he take out the trash, which I usually end up doing, and the dishes as my sensory issues will cause full meotdowns when I do them. On the days that my fiance gets home around 6-7pm, I will often be taking a nap with our daughter because I get maybe 3-4 hours of sleep at night, and so he'll leave me sleeping (despite me repeatedly telling him to wake me up when it happens) until our daughter wakes up, at which point he complains that it's now too late for me to make dinner, and he suggests that we should swap dinner and dishes duties. This would mean pretty much only eating frozen or canned meals and spaghetti with plain tomato sauce like once a month as a "treat". Plus he's constantly telling me I hold our daughter too often, and need to let her just cry more. I shouldn't be going places with her without consulting him first, even though I literally only ever go to the store/mall or visit my aunt or mother with our daughter. He also hates when I have visitors because "the house is a mess" ESPECIALLY if those visitors are there to help me get some housework done because I struggle to get it all done while taking care of our daughter. And then just this morning at 4am he was getting upset that she was fussing because I couldn't hold her as I had to express because I was painfully engorged in one breast even after breastfeeding, so he went to sleep on the couch and came back up once the baby was quiet, which took three times longer than it would have if I was able to express without having to stop every 30 seconds to give her the pacifier. Then he has the audacity to say I should've just waited to express until 7am when she got up for the day. This man is driving me crazy and it feels like he doesn't care how much I do to keep our daughter happy and alive and keep our household running as smoothly as I possibly can.