Does the dad also stay home after a new baby?

I (31f) am having a baby with my husband (33m) we recently got into a bit of a tiff because he mentioned requesting days off of work for our birthdays (we usually take a trip) I mentioned he should save some days to be home with our newborn, he thought it was the most absurd thing ever. He said why should he, since he will be home to help me after work. I was very disappointed by this, I won’t really be alone everyday as I do have family in the area but idk I thought it was normal that the father would be home for a few days after giving birth. Is that not normal?

TL/DR: do new fathers typically take a few day’s off work to be with wife and newborn baby?