Or live-in-lover, or baby daddy, whatever. If it's half his kid, he's not your babysitter.
Have you ever heard women extolling how fantastic their partners are by bragging that they "help out" with the kids, or "babysit" so they can go out with the girls. Have you heard mothers-in-law beam proudly at dutiful sons-in-law because they are "such a helper" with the children. Attention please: men are not assistants to their mothering wives or girlfriends. They are 50% responsible for the kids, they should put in 50% of the work, and when they do, they should be seen as good parents, just like their partners, not more so because they pitched in.
I agree with Straight Dope Dad when he explains, "It is insulting to both dads and moms to call it babysitting when a father is taking care of his children." (Although he is a bit harsh with moms stepping down.) It is a stereotype that fathers are only around to assist and give moms a break every once in a while, but in many household the stereotype rings true.
Watching A Baby Story the other day (don't judge, it was on) I noticed moms, who had just gone through what I can expect were the horrors of labor, want to nap, but are worried about leaving the newborn alone with its father. One new mommy explained, she "let" her husband take care of the newborn during her naps, which apparently made her very nervous. She went on and on about how he was such a helper. It made me very sad.
I've stepped off my soapbox for now. But for serious, he is not your babysitter! And now that I've surely galvanized you to notice such a nuanced injustice, I'll send you here to look at a grass bridge. For serious, it's made of grass!