I actually disagree with this a bit. ( Not on you, I just chose your post)
I think the 'uneven distribution of parenting ' as you put it is normal and good at that age.
A baby has a primary caregiver, there is a reason we have that term. They have a primary bonding relationship.
It's not always the mum, but if at all possible, it should be the mom.
Biologically speaking a baby is primed to bond with and need their mother .
It's entirely natural and necessary that a child has a so called default parent before 1. Thats the start to secure attachment.
I do agree that it is all consuming and can be overwhelming for an (especially first time) mum.
And absolutely, dad can put baby in the pram and walk to the park for an hour so that mum can have a shower or some alone time. Or do bath time once in a while.
However I always say, reframe it a bit. Op, your contact hours with baby is going to be more. Don't try to fight that. Lean I to it.
I get to breastfeed and be my baby's one and all. Instead of resenting dh, do you know how much he is missing out on?. It isn't nice to hold your own child and them crying for their mum. But a dad shouldn't be competing for a baby's attention. It's normal and natural for a baby to want their mother. And it's so beautiful to be able to provide that.. hard, yes, but in a way you have a bonding with baby that her father won't have with her for at least another few months or the first year.
To be completely honest, 80% of everything to do with they baby falling on the mom on mat leave sounds about right to me. I would even say up to 90% for such a young baby. If you look at childhood development, a dad or grandmother or whatever should pick up the slack from the house and everything other than the baby. They should be freeing mums hand so that she doesn't have to cook or clean or do shopping, they shouldn't be having the baby 50-50.
And I know that's the new narrative in today's time. 'a dad is also a parent, he should do 50-50.'.
That's not ideal though. A young baby needs their mother and is absolutely hardwired to look for her.
So I just wanted to reframe that in your mind that having more contact hours with your baby is so developmentally advantageous.
Can you have a nice chat with dh and ask, hey darling I know she struggles to settle with you but I'd love 45 minutes, can you walk to the park ?(babies love the outdoors and generally sleep well when our especially when moving ie in stroller or baby carrier)
But I wouldn't be necessarily asking him to take DC when she cries or giving her a bottle unless absolutely necessary. When she cries she needs mum
And thsi will change, as children grow older and approach a year the spread can be more equal, but it won't be for now.
Then just my opinion and not based in fact (as above)😅 I think him working full time and doing cooking in cleaning is quite a feat. No because he is male, but because he works full time and takes on all domestic duties. It's also tiring.
Again just me, but at 3 months post partum I wouldn't be expecting a partner that work s full time to take on 100% of those tasks. First few weeks yeah, but if I'm on mat leave I do a bot more of the housework unless baby needs me.
That's just me, but might give you an idea that your setup isn't necessarily common.
Also I wouldn't think it funny of my dh brought a gaming console, but that's because of my stance on gaming in general😂
However it is often quite isolating for a new dad as they feel very inadequate and useless, so using his free time isnt unreasonable. It is a bit depressing to make him sot around and not get on with anything just in anticipation that you might need help.
I mean we've all been there in the middle of the night, up and breastfeeding a baby and looking over at our peacefully sleeping dh thinking ' you absolute bastard, how dare you sleep like a log and I be up'
But really what would it achieve to wake him? He has work in the morning, I can take a short snooze with DC in the day, what would it help him to also be up and look at me while a breastfeed? To change the nappy? That takes 30 seconds, it doesn't really add to my awake time.
Let him sleep so he can better handle my irrational sleep deprived moods in the morning.
Good luck op, it gets easier!!!