That is a good question about how the kiosks treat mixed foreign-US couples, not to mention same-sex couples. The link from CBP doesn't address either situation.
I'd say just make a game-time decision regarding whether to use the same kiosk. You could always just give it a try - either the computer will let you process together or it won't. My guess is that it will work given the large # of foreign-US couples that use JFK. And if not one of you can always step aside to another kiosk. Definitely Let us know what happens! I am curious.