house husband vs househusband

house husband and househusband both are nouns.

Word	Noun	Adjective	Verb	Adverb
house husband	Yes	No	No	No
househusband	Yes	No	No	No

As nouns, house husband and househusband are synonyms defined as:

house husband and househusband: a husband who keeps house while his wife earns the family income

house husband (noun)	househusband (noun)
a husband who keeps house while his wife earns the family income	a husband who keeps house while his wife earns the family income