I found out today they were both portrayed by Ann Morgan Guilbert. from The Dick Van Dyke Show and The Nanny for those who don't recognize the names

Yep, there is one episode of The Nanny where she calls Bryton Ritchie and she looks into a mirror and says "There's Millie" ! I'm sure most watching it when it aired did not get the reference, but us boombers got it :D

There's another where Fran wonders why Millie never got a spinoff, and Yetta answers she heard the actress was very hard to deal with.