Schedule chores. For instance, Mondays and Wednesdays, Dad's on morning duty. Or, you take every morning and he does bathtime or oversees homework.
Divvy up. The minutiae of kids' lives need managing. One of you might deal with scheduling all the details of your son's soccer practices and carpools, while the other handles doctor and dentist appointments and school field trips.
Stay out of it. If you've agreed that your husband is in charge of dinner on Wednesdays, don't object to repeated grilled sausages. If he's handling the acquisition of four egg cartons for a preschool project, say nothing about the bowl of eggs in the fridge. In turn, he's not allowed to question your "no food in the living room" rule if you're responsible for vacuuming.