The usage comes from the reciprocal relationship of the two people separating the people in question, such as two men who are each father-in-law to one the parents of their grandchildren.
co-in-law (plural co-in-laws)
- (rare) A distant in-law: A relationship by marriage with a separation by three degrees (two people), compared to prototypical in-laws, where the separation is two/one. The separation may be two degrees of blood kin and one of marriage (addressing the mother of the husband of one's daughter) or one degree blood and two of marriage (addressing the wife of the brother of one's husband).
- Depending on context, the term may be understood to mean specifically co-sibling-in-law, or co-parent-in-law.
- My co-in-law and I took our granddaughter to the zoo. [= co-parent-in-law]
2006, Ernest S. Burch, Jr., Social Life in Northwest Alaska: The Structure of Iñupiaq Eskimo Nations, page 94:
- the co-in-law, or aŋayunġuq-nukaunġuq relationship, which involved people who married siblings [= co-sibling-in-law]