Jeffrey grew up in New York City, where he began his career at age twelve acting professionally off-Broadway.

He began his film career working with some of the most respected filmmakers in the business, on such films as Marjoe (edited by Larry Silk, Academy Award®, Documentary Feature, 1972) and William Friedkin's The Exorcist (1973). He apprenticed with the legendary editor Dede Allen on the Arthur Penn segment of Visions of Eight (1973), and assisted Thelma Schoonmaker on Martin Scorcese's Raging Bull (Academy Award®, Film Editing, 1980). 

Jeffrey began editing on the NBC prime-time documentary series Lifeline (1978). He was associate editor on director Carroll Ballard's feature Never Cry Wolf (1983). He has edited numerous documentaries for television, starting with the PBS documentary Faces Of the Enemy (1987), for which he also received a co-directing credit. He edited the short HBO documentary Kings Point, which was nominated for an Academy Award® in 2013.

Jeffrey first worked with Rob Epstein consulting on The Times of Harvey Milk. In 1987 Jeffrey and Rob formed their production company Telling Pictures and began working as a filmmaking team.

Together Jeffrey and Rob produced and directed and Jeffrey co-edited Common Threads: Stories From the Quilt (Academy Award®, Documentary Feature, 1989) and The Celluloid Closet (Emmy Award for directing, 1995). They also produced and directed Paragraph 175 (Sundance Film Festival Documentary Jury Prize for Directing, 2000). Their documentary feature And the Oscar Goes to premiered on Turner Classic Movies in February 2014. 

Their first scripted narrative film was HOWL (2010), which Jeffrey and Rob wrote and directed. HOWL, starring James Franco and featuring David Strathairn, Jon Hamm, Jeff Daniels and Mary-Louise Parker, premiered on opening night at the Sundance Film Festival, followed by the Berlin and London International Film Festivals. It was released theatrically and on home video by Oscilloscope Laboratories in the U.S. and internationally by The Match Factory. HOWL received a 2011 Freedom of Expression Award from the National Board of Review.

They next directed Lovelace (2013) starring Amanda Seyfried and Peter Sarsgaard, featuring Sharon Stone, Robert Patrick, Hank Azaria, Bobby Cannavale, Chris Noth, Juno Temple, and James Franco. Lovelace premiered at Sundance (where it was quickly picked up by The Weinstein Company/Radius-TWC for U.S. distribution) and at the Berlin International Film Festival. 

Jeffrey has taught documentary directing in the graduate program at Stanford University, and editing at California College of the Arts. He is a member of the Directors Guild of America as well as the Academy of Motion Picture Arts and Sciences' Documentary Branch. He is co-author of The Art of Nonfiction Movie Making, published by Praeger in 2012.