What is a good schedule for sharing nighttime responsibilities with my husband?

Night schedule. I recommend getting your newborn on a 10 pm, 2 am, 6 am feeding schedule if possible. Mom and dad can rotate the 2 am feeding every other night to allow every other night sleeping 8 hrs. This works for most infants as early as 4-8 weeks if term baby. I also highly recommend mom napping once a day with the baby during the first 2 months if possible.
Take turns. Take turns responding to your crying infant. If you are breastfeeding, dad can get the baby, change the diaper and bring him to you to feed.