Organise a day for your DD to go out without either of you for a few hours. Nominate a few chores for your man to tackle and you do the others.
Its half his mess so half the responsibility SHOULD be on him, none of this "I make the money so you keep house" crap ... you're raising his child thats work in itself.

SO,

Get the house in ship shape.

Then do 1 thing every day while your LO sleeps and do the dishes at the end of the day so you wake up to a fresh clean kitchen (start) every day.

I try to vac every 2nd or 3rd day, toilet scrubbed once a week but properly with stuff once a fortnight (I struggle with the smell of disinfectant atm), I wash every second day (nappies) and clothes just as we need them. I fold as I bring things off the line before they get in the basket and try to put them away immediately though that doesn't always work.

I don't dust often but there is little point getting anal about dirt where I live. I don't have a routine as such just do things as I see they need doing.

Its much easier to maintain a little bit at a time so get the bulk of it done and then just do 1 job a day.