Doman was born in Philadelphia, Pennsylvania, and is an alumnus of Northeast Catholic High School. He is a 1962 graduate of North, an All-Catholic League football player and a member of the school's Hall of Fame. He received a Bachelor of Arts degree in English Literature from the University of Pennsylvania in 1966. While at Penn, he was a three-year letterman and starting defensive back with the Quakers football team from 1963 to 1965. He also earned a Master of Business Administration degree in marketing from Pennsylvania State University in 1972.

In between his time at Penn and Penn State, he served with the United States Marine Corps, beginning with his enrollment in its Officer Candidates School at Quantico, Virginia. He was commissioned a Second Lieutenant in March, 1967 and served with the 3rd Marine Division in the Vietnam War.

After graduate school, he spent nearly two decades in the advertising Business, beginning with SSC&B Advertising and Norman Craig & Kummel. He was one of the first six employees at TBWA New York when it debuted in 1977. He concluded his fourteen years with TBWA as Executive Vice President, Head of Business Development responsible for a new Business program which resulted in Agency of the Year honors from Adweek in 1990. He transitioned from advertising executive to full-time actor when he was cast in a commercial for AT&T in 1991.

Doman had cameos in the 1997 film Cop Land and the 2003 film Mystic River. He also had a role on the film The Opponent. Doman also had a small part in the 2010 film Blue Valentine. In 2004, he appeared in the third installment of action film series Sniper.

From 2010 to 2011, Doman appeared in three episodes of Rizzoli & Isles as a mob enforcer, reuniting him with Sasha Alexander. The two had previously appeared in NCIS in the Season 2 episode "Doppelganger", where Doman played Lt. Cheney, the head of a local civilian law enforcement while Alexander played Special Agent Kate Todd.

On television, Doman has guest-starred in the Star Trek: Deep Space Nine episode "Shakaar". He also portrayed Dr. Carl Deraad on Seasons 5 and 6 of ER, and bad-guy CEO Walter Kendrick on Season 2 of Damages. He provided the voice of Don Morello in the video game Mafia: City of Lost Heaven. Doman also provided the voice of Caesar in the video game Fallout New Vegas. He also played a small role in the action film Die Hard with a Vengeance, as one of the site managers for the construction of a tunnel featured in the film. Doman starred as Rodrigo Borgia in the 2011 historical drama series Borgia by the French premium-pay TV Canal+ and the German ZDF and starred in Director Pieter Gaspersz's AFTER opposite Kathleen Quinlan.

Doman has been the voice for Michelin tires and Home Depot and in 2013 began narrating videos for the Philadelphia Eagles. He currently plays the Mafia Don known as Carmine Falcone in the series Gotham. He also played Senator Ross Garrison in Person of Interest and Helen's (Maura Tierney) father in the Showtime drama The Affair. He recently appeared in Season 3 of the Netflix show House of Cards as Bishop Charles Eddis. He plays the U.S. Ambassador to Germany in Season 2 of Berlin Station.