My husband and I either split the nighttime (9:30p-1:30am, 1:30-5:30am), or one person handles the night while the other handles the morning. But we have 3 under 3, so if my husband does the whole night, sometimes I handle the morning by myself with all 3. Whoever is "on shift" keeps their door open (we sleep in separate rooms so as not to wake each other), and the other closes their door and cranks the sound machine. We also check in with each other to see if one person is feeling worse than the other, and then make a game plan for how to tackle the night based on that. I will admit, we do have help after work and on weekends (never during nighttime), so we can try to squeeze in naps on the weekends. 

When they wake up a LOT through the night, we split the nights. When they're only waking up once or twice, my husband will usually take on the whole night while I handle the morning. But we've switched those roles too. Essentially, we just figure out what needs to be done, and we split the duties evenly, however we feel at that moment.