@aihi Lurker pre-mom here. We're due with our first in April. I get two weeks paid and have to take anything else unpaid. My husband gets zero days, so he'll be using one, maybe two, weeks of his three weeks of vacation. Neither of us is eligible for FMLA.
He does work from home, but is in sales for a company with manageable but still pretty demanding metrics, so a) he can't slack off and b) in sales, the work you do today affects your success and pay months down the line, so we couldn't afford for him to be away from his phone for very long anyway. We don't have a ton of help as my parents are both still working and his aren't in the picture.
The idea of birth doesn't really scare me. The idea of recovering on my own with a newborn after he goes back to work only a week in gives me the same feeling in my chest that my PTSD used to.
Take all the time your company allows. Some of it might be for you, but most of it is for your wife.