The bittersweet love story opened to rave reviews, and captured eight Tony Awards including best musical direction and the top musical prize in June.
Kazee plays the guitarist role that Glen Hansard played in the film, won the best actor in a musical award for his performance. Milioti is the musical's female lead, originally played by Marketa Irglova.
Be sure to tune in to "CBS This Morning," Thursday 7-9 a.m. ET, for their full live interview.