house husband vs married man

house husband and married man both are nouns.

Word	Noun	Adjective	Verb	Adverb
house husband	Yes	No	No	No
married man	Yes	No	No	No

As nouns, married man is a hypernym of house husband; that is, married man is a word with a broader meaning than house husband:

house husband: a husband who keeps house while his wife earns the family income
married man: a married man; a woman's partner in marriage

Other hypernyms of house husband include hubby, husband.

house husband (noun)	married man (noun)
a husband who keeps house while his wife earns the family income	a married man; a woman's partner in marriage