"Affine" is a noun meaning "relative by marriage" - in other words, any of the in-laws. The adjective form is "affinal".
The word comes from the Latin affinis, meaning "related". This is the same word "affinity" is derived from. For some reason, however, "affinity" caught on as a relatively commonplace word, while "affine" is never used outside of anthropological works. (Weirdly enough, Webster 1913's first definition of affinity is "relationship by marriage" - so it seems the term for the relationship was once in general use, but the term for the relative never was.)
Still, I think "affine" is a much better term than "X-in-law". It's also a good one to tack on to "fine" when playing Scrabble.
Moving from the merely obscure to the completely arcane, the technical term for the other kind of relative - relatives by blood - is "consanguine". Another good one for Scrabble, and not much else.