Fraternal matrimony 

An intense emotional relationship between two heterosexual males that, while non-sexual in nature, exceeds the boundaries of a traditional bromance.

A year after pledging the same fraternity, Harry and Gabe reached a state of fraternal matrimony and became the envy of their fellow brothers.

Fraternal matrimony is legal in California.

Fraternal matrimony by King Bro July 1, 2009