Similar situation, although no cleaner.
Washing laundry yes, I do all of it.
Cooking I do 90%, he does ‘special’ meals sometimes, but bit randomly. When my daughter was a baby/toddler, DH did all the cooking at weekends. He never did a night waking though and there were several a night for many years. So it depends on your situation. (If you’re up all night with a screaming baby you have basically worked all night and shouldn’t be expected to do 100% of the house stuff in the day! Butnif your child sleeps through, it may make sense.)
Clearing up is more blurred… It’s very important for your relationship that one of you isn’t constantly cleaning up after the other. I had to train DH that I will empty laundry basket, but I will not walk around the house collecting his dirty laundry from wherever he feels like leaving it. Similarly I’ll do the dishwasher load / unload / wash the stuff that can’t go through it, but I won’t collect his empty plates and cups from wherever around the house he feels like leaving them. I won’t rehang his towel if he lives it in a damp pile on the floor. Etc.
Being a SAHM is wonderful when they’re a baby/toddler, but it can slowly damage your relationship, as your husband becomes part of your job and another thing constantly demanding food / needing to be cleaned up after. Similarly the working partner may find themselves less attracted to their food-stained partner who now lives in PJs. It’s all very unsexy stuff on both sides.
Not saying don’t do it - it’s wonderful for the children and very stabilising for the family and I don’t know how we’d have survived 2020 if we’d both been working - but discuss and agree what’s fair re money and housework in advance, and if you see the situation damaging your relationship do consider changing things. Also watch out for isolation and depression they creep up on you when you don’t have colleagues/income and no one ever says thanks or well done and strangers constantly imply you’re lazy.