Greene is a music professor at Western Connecticut State University, and he resides in nearby Sandy Hook, Connecticut; he also taught at the University of Manitoba for a three-year stretch. He is married to flautist Nelba Márquez. His daughter, Ana Grace Márquez-Greene, was six years old when she was murdered in the Sandy Hook Elementary School shooting, and the album "Beautiful Life" was made in tribute and dedication to his daughter. He is part of the music ministry at his local church, Glory Chapel International Cathedral.