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If the character is male, see also: Henpecked Husband.
Awful Wedded Life is a genre of domestic comedy according to its description and Henpecked Husband is a character trope, not a theme or plot device trope.
Hmm, well, Awful Wedded Life has some very non-domcom examples (A Brother's Price, A Song of Ice and Fire, etc). The gist of the trope is the same for what you're looking for. I think it just needs a description update noting that it can be played for laughs or drama, and is not restricted to domestic comedies (although it did get its start there).
I'll mention Awful Wedded Life on the Trope Description Improvement Drive forum.
Is there a page for the Inverted Trope of Happily Married, where characters are unhappy in marriage? And if that's too specific, is there a trope for where marriage in general is painted as miserable?