A romantic (or possibly platonic) relationship between two individuals that is heavily antagonistic- a dynamic laced with far more frequent arguments and verbal altercation than what typically comprises a romantic relationship. Most used in reference when the altercations are over inane matters.
"So what are Alice and Frank arguing about this time?"
"Apparently he ate most of the green M&M's, and I guess those are her favorite..?"
"Sheesh, that's even more petty than yesterday's argument. They're in such a foemance..."