married man vs better half

married man and better half both are nouns.

Word	Noun	Adjective	Verb	Adverb
married man	Yes	No	No	No
better half	Yes	No	No	No

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

Other hypernyms of married man include adult male, man, married person, mate, partner, spouse.

married man (noun)	better half (noun)
a married man; a woman's partner in marriage	a person's partner in marriage