They have their own way.
As new mothers we can be a bit overprotective of our babies. There is so much desire to get it right, we forget that most of the time we are just flying by the seat of our pants. After a few days, or weeks, or months, we have figured a few things out that work for us. And we start to micro-manage our support.
"No honey, hold her the other way."
"You have to get the wipes out first."
"Get to him faster."
"You're not doing it right!"
We nag and criticize our partners out of helping us. Every time they do something, they do it wrong. So better to stay out of the way, or just go sleep somewhere else. A year goes by and we wonder why we are doing it all alone.
The best thing you can do as a parent is to let your partner figure out what works for them. The relationship and care is going to be different. It needs to be different. If you find yourself wanting to step in simply say, "Let me know if you need anything." If you can't stay out of the mix, then you have to build in time to leave them alone. You complain about not getting enough alone time anyway, so leave your child with their other parent and get out.
The bond they will have will be so much stronger. Your relationship will be more equitable. You will be happier.