The way we worked it was that when Dh was home we were a team, both on duty at the beck and call of the children. We got things done then could sit down together. Dh had a lie in on a Saturday having worked 5 days straight, I had the same lie in on a Sunday. This meant Dh got one on one time with firstly one child (newborn) then both of them, we have a 3 year gap. Often he would take them out for breakfast known as The Boys' Club as we have sons and I am the only female in the house. They were a little gang and it was bliss to lie in the bath knowing there was no one else in the house.
If he was going anywhere, shops, tip tun, B&Q then he would take a child with him. This meant he got one on one time with each child doing the shitty jobs with a child. This has benefits when they are older that they start to understand what is involved in any DIY projects at home. Plus I had to do this before the children were in school with two of them and every half term and summer holiday.
I batch cooked as in massively, so a 6 portion chilli (food processor is your friend) which was chilli with rice but then served with nachos and sour cream, same with bolognaise first served with just pasta but then served as ziti. Everything had a dual purpose. I was able to batch cook as Dh was on hand with the children or helped me batch cook.
Look, I saw being a sahm and the house as my job, that job meant coming up with a schedule for laundry/housework and I had a 3 week menu plan with a 6 week swap out. Supermarket food was delivered but I had a list of things to buy in a spreadsheet for the meal plan so no thinking ahead. That removes some of the drudgery and mental load. Dh would make lunches and dinner on the weekends because he was here to do that. I did weekdays as the children ate earlier. We also used a slow cooker too.
Dh and I also tag teamed, if one of us needed a break the other happily gave it because it was reciprocal and neither of us took the piss, half an hour was half an hour. Dh was raised by an amazing sahm and a hands off Dad. He didn't want that for his own children. Even now we don't have phones in our hands when we talk to each other, we regularly ask is there anything I can do that would make your life easier? Dh was always on hand for the morning get ready for school routine.
This comes down to expectation and communication, that is why we phrased it as can I do anything, not can I help nor you never do this or that. It has always been positive, same as with children when you talk about the behaviour you want to see. Dh has always thanked me but then I thanked him for providing this life for us too, this house, my car, I am grateful and so is he for clean clothes, meals cooked etc.