He has conducted numerous Broadway and Off-Broadway shows, including How the Grinch Stole Christmas!, Wonderful Town, Falsettos, Miss Saigon, and Anything Goes.
He served as pianist and associate conductor for the hit 2022 Broadway revival of Stephen Sondheim and James Lapine's Into the Woods, and can be heard playing on the Grammy-winning original cast recording.
Rosenblum wrote the songs and incidental music for Quincy Long's play The Joy of Going Somewhere Definite, which ran Off-Broadway at the Atlantic Theater Company in 1997.
Also along political lines, Rosenblum wrote book, music, and lyrics for Mark Felt, Superstar, which tells the story of the Watergate scandal from the perspective of "Deep Throat," the FBI official who was the secret source for journalists Bob Woodward and Carl Bernstein of the Washington Post.
In February 2016, the Royal Central School of Speech and Drama in London presented a devised musical theater work consisting of Rosenblum's songs, entitled "Love is Not a Science".
As a result, the Central School commissioned Rosenblum and Lessner to write a new musical, based on the play Stage Door by Edna Ferber and George S. Kaufman, which received its world premiere production in May, 2017.
His book Closer Than Ever: The Unique Six-Decade Partnership of Richard Maltby, Jr. and David Shire was published by Oxford University Press in June, 2024.