family vs broken home

family and broken home both are nouns.

Word	Noun	Adjective	Verb	Adverb
family	Yes	No	No	No
broken home	Yes	No	No	No

As nouns, broken home is a hyponym of family; that is, broken home is a word with a more specific, narrower meaning than family:

family (noun)	broken home (noun)
primary social group; parents and children	a family in which the parents have separated or divorced
people descended from a common ancestor
a social unit living together
(biology) a taxonomic group containing one or more genera
a collection of things sharing a common attribute
an association of people who share common beliefs or activities
a loose affiliation of gangsters in charge of organized criminal activities
a person having kinship with another or others