He's being a selfish dick!
He is not being a good father and he is not being a good partner
Good fathers and partners make an effort with their dc not just the fun stuff/when it suits and they don't wait until mum is on her fucking knees with exhaustion to pay lip service up pulling their weight!
I'd be reading him the riot act!
My ex was army (and in a role where you have to be extremely alert!) and only had 10 days annual leave when dd was born. I was on mat leave/Sahm until she was around 1. Then I returned to working as a childminder.
If he hadn't pulled his weight when he was home I would NOT have been at all impressed!
He used to either take baby when he got home from work or he'd take over whatever chores needed doing.
I was bf for most of 1st year but he'd still be up when I/baby was, he'd fetch me drinks, blankets, dressing gown if needed, when I had finished feeding if needed he'd do the nappy change.
When she woke early he'd get up with her as he had to be up early anyway, he incorporated her into his exercise routine of a morning which she loved.
Then he'd hand her over to me as he was setting off for work
You are BOTH baby's parent, you BOTH need awake down time and the same amount of sleep each - does he think a vagina renders you not needing as much sleep?! Prat!
I'd certainly advise you have no more children with him unless he changes his attitude and behaviour!
frankly he should have at least been doing the weekends to give you a break! What you've written means that for the 1st year you NEVER got a break?
Utter bollocks he "can't" do it of course he can he just doesn't want to and thinks your sleep, your wellbeing, your health is LESS important than his!
I'd point blank ask him if that's what he thinks and if so why! Let him tie himself in knots trying to explain that one!
Really this wanted nipping in the bud far earlier on, you certainly need to address it now so that all the future childcare doesn't fall to you too.
Does he take time off work if child is sick? Is he going to (you should share this responsibility) what about bank holidays? School holidays in the future?
As dd got older we split lie ins over weekends too he had the Saturday I had the Sunday
Has he ever been in sole charge of the child? If not that needs fixed ASAP too!
To be quite honest I'm very sceptical that he's pulling his weight elsewhere too, cos if he was he wouldn't be ABLE to sit on his arse come 8pm!
This is not the minor thing you seem to be viewing it as, this is a major issue and shows he doesn't care for you or baby as much as you think
He is naturally a night owl.
As am I - he can still work around that though I had to and many many other parents do too. If he's up late anyway he can do the late night/wee hours wakings
You don't need to respond to every murmur either you need to give it a minute and see if they settle back down, at that age they usually do
Does he do bathing/bedtimes? He should, not just to give you a break but bonding with baby too. How much time does he actually spend with baby?
My ex loved doing bath/bedtime, had great fun splashing about and it was his bonding time with dd.
He sounds pretty crappy as a dad and a partner tbh