What Do We Call our Children’s In-Laws?

Susan in Traverse City, Michigan, wonders if there’s a single English word that denotes the relationship between two mothers-in-law, two fathers-in-law, or a mother-in-law and father-in-law. Co-mother seems too vague, and the psychologists’ terms affine or co-affin e, from the same root as affinity, aren’t used widely among the rest of the population. In Spanish there’s consuegro, and in Yiddish machatunim, as well as words in Portuguese, Italian, and Greek, but nothing that’s been adopted into English, and the German Gegenschwiegermutter doesn’t seem a likely candidate, either. This is part of a complete episode.