Whining

I read To Train Up a Child when my oldest daughter was one. Now she is three. To most (who haven't read the book) she is a well-trained darling, but my husband and I are struggling with her tendency to whine.
So many have advised us to just ignore it and that it's simply because she is a girl and she just turned three and that's what three-year-old girls do. Arrgh! It's easy enough to deny her whatever she is whining for, like a toy or a treat. But just a second ago she looked at me and said, "My baby is crying. I have to go get him," in a loud, high-pitched whiny voice. How can I train her to talk with a "normal" voice? My husband loves to be with her, but finds that frequency unbearable. And a side note, I do not whine. : ) Thanks for any advice!