New Jersey Dean, the only organization that I can think of that is like this would be Alpha Nu Omega, Inc.
For the rest of the board, Alpha Nu Omega is a Christian GLO that is indeed both a fraternity and sorority.
One organization -- two parallel units.
I really don't see a problem in the males of the unit establishing the sorority chapter of the parallel unit, especially if there is one organizational unit nationally.
It is not like AKA and Alpha -- our organizations have a shared history and no official relationship administratively. Sigma and Zeta are constitutionally bound as brother and sister and perhaps share some programming, but they are administratively unrelated.
Check out
www.alphanuomega.org and send them an email. Ask them how they do this administratively. Hope this helps.