What do you call a married black chick with a kid? A single mum. lol
Is this how you see black people?
To me a broken family is when a man isn't present or when there are relationships problems which could be caused by other factors and blacks are broken.
Your joke assumes that black men are not there for their kids but that is not the case for most black men. Don't paint all blacks with the same brush and characterize them falsely because of skin color.