I will start this by saying I have never worked nights, so have no idea of the impact it has on your body and mind.
My Husband works 3 nights a week. He goes to work, comes home, sleeps, gets up, showers, goes to the gym and then back to work. I have accepted that I am solely responsible for everything on those days. I also work PT so this is a juggling act to manage kids schedules and get everyone where they need to be, go to work, and be back in time to collect them, he will help collect the kids if he is awake on time which helps massively. Then I cook dinner, do homework, bath, bedtime etc.
On the days he isn't working he doesn't seem to do anything during the day apart from look after our youngest but has energy for the gym and running errands that benefit him. He will do bits here and there around the house but tells me he is too tired to do anything else. I end up doing all the cooking and bedtimes. Sometimes I will ask him to help with bedtime for example and it is met with the least effort possible - not making the kids brush their teeth or following our proper routine for bed. My youngest in particular gets really upset as he likes our routine and its hardly arduous, its just teeth, pjs, stories and cuddles. Ironically following the routine takes less time to complete than what he is doing but is a bit more effort.
Weekends when I need help to reset things seem to be met with animosity and I am made to feel unreasonable that I need help with the house. He will do stuff but I have to nag.
We used to have a good routine where I could sleep a little bit later on some of the days he wasn't working but that seems to have slowly eroded to zero.
I have basically no time for myself. However he has the gym and also will go to the pub on his days off.
I have no idea if this is the norm, my mum used to work nights when I was a kid and would sleep whilst we were at school then do tea and homework before heading out again but I know she was shattered from this and much of it was because there was no other option. I don't want to force him to do stuff if he is exhausted but equally I think he's having me over!