Midler's first studio album in eight years will be produced by Marc Shaiman.
The show is created by Everett along with Marc Shaiman, Scott Wittman, Adam "Ad-Rock" Horovitz, and Matt Ray.
Everett's new show is written by Marc Shaiman and Scott Wittman, among others.
The new show opens the Public Theater's fall season.
The new show will play Joe's Pub.
Wesley Taylor, Adam Chanler-Berat, and Mitchell Jarvis will also participate in the 54 Below event.
Shaiman and Wittman were honored by the New York Pops on April 28.
The event will honor Hairspray and Smash composer/lyricist Marc Shaiman and director/writer Scott Wittman.
Shaiman will receive a grand tribute at Carnegie Hall on April 28.