What would my father call my father-in-law? Is there a name for this type of relationship?

My wife's parents are my father and mother in laws, and my parents are her father and mother in laws, in tagalog our parents are called mag-"balae", in ilocano "abalayan". There is no such English term for that.

balae
bal´ae n. parents and parents-in-law relationship (term of reference), a parent of one's son or daughter-in- law
http://www.tagalog-dictionary.com/cgi-bin/search.pl?s=balae

In Yiddish and Hebrew, the word "Mechuttanim" serves the purpose for referring to one's child's in-laws. The word best translates in English as "the married-into" or the "relatives by marriage". A father would call his son's father-in-law his "mechuttan". The word "choten", from the same root, is used toward the beginning of the book of Exodus, referring to Yitro (Jethro) as the father-in-law of Moses. In Modern Hebrew, a person would refer to his father in law as "chami", and to his mother-in-law as "chamoti".