When we had DS, DH was working full time and odd hours, but when he was home he held, bathed, burped DS after feeds, changed nappies. He cut my dinner up and put it within reach when I had milk-monster DS cluster feeding at dinner times
If he was having trouble sleeping in our bed because I was sitting up to feed DS he went off and slept on the sofa without complaint.
Once DS was 18 months old we 'swapped' roles - I went back to work f/t and he became a SAHD. We both read with DS. We both take him to the park, or out to the museum or wherever - we both make sure the other gets lie-ins when tired, he does most of the cooking through the week so I cook at weekends. We both do laundry, we both tidy and clean (admittedly he's less bothered by mess than I am so I'm more likely to dust or put things away but if I point things out that he's left lying around he'll put them away). We're both grown-ups, we're both parents, we're both living in the house generating mess, wanting nice meals to eat, clean clothes to wear, a happy son, so we both work at it.
A couple of people on here before have had some success drawing up a list of household jobs that need doing, roughly how long they take, and sitting down to have a good think about what's actually fair in terms of 'labour'.