I think early on with a new baby, both parents wake up more due to novelty than instinct. When you're used to not having a crying child in the middle of the night, suddenly having one takes some adjustment.
Since my wife nursed the kids, our arrangement was that she would be up with babies at night almost every time, and I would be up with them in the morning when they decided that 5am was time to be up for the day. Over time, I stopped waking up to baby cries at night, but I am now hyper-attuned to child noises from 5-7am.
Since my wife nursed the kids, our arrangement was that she would be up with babies at night almost every time, and I would be up with them in the morning when they decided that 5am was time to be up for the day. Over time, I stopped waking up to baby cries at night, but I am now hyper-attuned to child noises from 5-7am.