7 day old

We just had our first baby 7 days ago. Besides being sleep deprived, things are going well. My husband seems to think that we need to take turns and be up all night watching the baby. He thinks we shouldn’t both fall asleep when baby sleeps because one of us needs to be watching her at all times. He’s so scared of sids which I totally get, but I think we can both still sleep?

Is that the case or is it ok for us both to sleep while she sleeps?