Foreigner4Basicly there can be 2 versions of that story:
1) She does everything in the house, nurtures the baby, while he sits in front of the tv and expects her to serve him. When she wants a bit of time break from the chores for herself, he complains.
2) He works 12 hours per day, coming worn out from the buiding site and sees the same pile of dishes in the sink for several days. Of course there is no time for cleaning up the dishes but there is time for pilates.
Somehow my first impression was the latter (maybe the OP's nickname let me to assume so :), but of course I may be completely wrong. The point is that it doesn't always have to be stereotypical: lazy guys expecting women to serve them.
You surely don't realise how difficult it is to try to do something with a tiny baby strapped to you. Babies DO NOT sleep all day.
You are right, I don't have a baby. But the guy might think so (that a 3 month old sleeps all day). That's why the best solution would be if she sincerly talked about it with him. Maybe doing an experiment and let him to care a baby for a whole day and see how he'd manage, make him to realise that's not an easy task.