Op, you are being taken for a mug,
either both parents happily and equally meet their children's needs, without having to be asked by the other, or one parent is taking advantage of the other,
asking him if he has a special reason for being pathetic and if he has any intention of changing,
oh and his hours are neither early nor long,
If he lived on his own, he would still have to clean, cook, wash up, load machines,shop, just because he is in a relationship it doesn't mean he can opt out of doing these things,
print out a list of every single task that happens in your household(keep adding any you forget), including breast-feeding, don't ask him to do anything just add your initials next to every job you do,and a tally mark for how often you do it, let the evidence to his laziness stare him in the face, every time he walks past it on the wall,
Don't waste any energy trying to get him to do what he should be naturally doing, he has to decide if he cares how his partner views him, and step up,
if he can't be bothered, then you have your answer, he views you as a push over, push overs become doormats, doormats become bog brushes.
good luck.