If this is your first child, you need to both sit down immediately and discuss taking turns overnight. You both need sleep. But don't make it a battle with "I slept less; I'm winning the sympathy war". You're both adults (I assume) and you need to lay out terms for taking turns. If one of you is breastfeeding, (since your genders aren't mentioned and BFing is unfortunately one side if it's a newborn and you can't pump yet) the other should put back to sleep after/wake up next. Talk about how long feeding takes and that you're up with them. Formula, take turns with that too obviously! Taking turns still counts when they're older (but under 1) and still waking at night. You're both awake during the day, you both need sleep at night.

They and them refers to more than one person regardless you should run the other way now while the kid is a baby