The father has so many roles during and after the birth of a baby. It sounds obvious, but you should prepare for the fact that you need help, and a lot of it.
A woman after giving birth is in pain, fuzzy, flooded with hormones, excitement and fatigue. The first days are accompanied by bureaucracy and if your partner doesn't have too much free time - it can definitely become your job. Amidst all the hustle and bustle, don't forget to take a moment to look at the life you've created with your new family.