In the US, common practice has been for the newborn to stay in a special ward, under constant surveillance by nurses, for as long as he needs to stay in the hospital. The newborn would be brought to the mother's room for short periods, for nursing, for "bonding time," to show off to visiting relatives, etc. No way would the infant be left in the mother's room while the mother slept.

My son was thought to have a respiratory infection, so he was kept for a week to complete a course of intravenous antibiotics. My wife & I were encouraged to spend as much time as we wanted with him. My wife, once she no longer needed care, moved into a room in the hospital that was set aside for parents of hospitalized children. I think we had to pay for this room out of pocket, but the cost was comparable to staying in a motel.

Consequently, I don't know what the "normal" stay is. Anyway, this was 23 years ago.