As a former stay at home parent, my answer to this is: it depends. Definitely do a weekly check-in and listen to what your partner needs in that moment.

My needs changed a lot over time (sometimes week-to-week!) especially as a breastfeeding parent. Kids go through developmental stages which can be anywhere on a spectrum from delightful to really really frustrating for the one who is with them all day (and perhaps night!). Whenever my husband checked in with compassion and the intention to support, it was helpful.

In terms of the practical, some weeks I needed things like help with making food (which in my husband's case meant getting takeout! 😂) or taking an extra task that was typically mine. Other times it meant listening to me vent.

We also have assigned parenting duties (he's the bather and evening toothbrusher) which typically bought me 20 minutes every night, and a "mandatory" "give mom 2 hours alone" period no matter what on either Saturday or Sunday. Alone time is something I need to function, but it's hard to come by as a SAHP. Your partner will need to hold boundaries on taking what they need when it comes to time for themselves, which may be particularly hard if the little one (or ones) has a strong preference for them. I personally really struggled with this both when I was a SAHP and even now that I'm back to work.

And please be real with yourself. There's no such thing as "even" in a partnership. Sometimes you're giving more and sometimes you're taking more. Striving towards an equitable relationship is admirable, and your partner is lucky to have someone like you!