married man vs married person

married man and married person both are nouns.

Word	Noun	Adjective	Verb	Adverb
married man	Yes	No	No	No
married person	Yes	No	No	No

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

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

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