Also called "Muttrimony." I'm still not entirely sure why, but seeing articles like this one makes me apoplectic. Perhaps it's because the same representatives of the clergy have such difficulty wedding two entirely human males or females.

“Well, I am a reverend,” Scott said. “If you’re in a family with two animals and they want to unite in a wedding, what difference does it make? It is not a sign of the Apocalypse. It is a sign that animals often seek to form a lasting bond and have deep commitment.” (read more)