@AssumeItWasSomethingClever I might not be the best person to respond to your post as my tolerance for dads thinking they have a genetic right to act differently to mums is currently at zero but your husband sounds like a dick (sorry).
The nice way to answer is probably that he struggles with him being so unsettled and it makes him feel like he's a bad dad so he wants you back involved ASAP because you know what you're doing.
But - bullshit (sorry again). You know what you're doing because you have to, you don't get the luxury of palming him back to someone when he gets fussy. Dads don't get to just swan in when the child is 4 and mobile, toilet trained, verbal and more emotionally stable. Or when it involves standing outside on cold winter mornings watching sports they'd happily spend 90% or their time watching anyway.
If looking after a baby is so easy that you can have time to clean the house and make his tea and be pleasant about it - why isn't he jumping at the chance to take over when he gets in from his "oh so stressful" day at work?
In terms of actual practical help - I'm not sure how you best work, but I have a very logical brain and I love lists and instructions. For example - cleaning the house, I always feel like I have to do the whole thing in one go or it's a pointless exercise, but I've been following 'The Organised Mum Method' (I really dislike the name ha) and she basically splits tasks between days, and it should all take you no longer than 45 mins. Because someone is telling me "it's Monday so it's just the living room", I can follow those instructions without having guilt for the rest of the house. The idea is because you're doing the same tasks in each room each week, eventually it becomes quicker to do e.g first time you do it it might take a while because you may not always clean the skirting boards, because you're then doing them every week, they become much easier to clean.
In terms of baby - if he needs 100% or your attention - give him it (obviously not at the detriment of your mental health or anything. If your husband has issue with that then ask him what he thinks the solution is.
And for you - If I were you I'd buy some noise cancelling headphones - put them on when you're in the bath and set a timer so you get a full hour. Again - if your husband struggles to have the baby for an hour - ask him to imagine doing it the other 23 hours of the day and now does he see why you need an hour to yourself?