Children staying in hospital with you after you give birth?

Alright so I have a 9 year old stepson and I try explaining the concept of having to be in the hospital for a few days after having my little girl with his father staying with me during that time. I told him he could come visit as long as he wants to, but that he wouldn’t be able to stay the night because that is what I’ve heard. My boyfriend seems to think I’m mistaken and that after I’ve given birth my stepson should be able to spend the night. Any advise here?