counterpartner
n.— «Have you chosen a new name for your relationship with each other? My sister calls her former husband’s current wife her “wife-in-law.”…We often refer to each other as “counterpartners.” A counterpart is someone with whom you share similar responsibilities—and we do in regard to the kids—but we also regard ourselves as “partners” in taking care of the children. Hence, we are “counterpartners.”» —“Here’s one way to introduce your ex’s current spouse” by Jann Blackstone-Ford, Sharyl Jupe Mercury News (San Jose, California) June 15, 2005. (source: Double-Tongued Dictionary)