Martinez got his chance when he landed a role on ABC's daytime drama "All My Children" and then went on to win "Dancing with the Stars," helping America see beyond his scars and disfigurement.
"If we let that narrative be simply about victims or heroes, I think we've missed an opportunity," said Mike Haynie, executive director of the Syracuse's institute. "Most veterans are somewhere in the middle of those two extremes."
At a panel sponsored by the institute about Hollywood's influence on America's perception, David Gale, formerly of MTV and now the co-founder of a veterans-focused production company We Are the Mighty, said, "We need more volume. We need more stories. We need to be able to show veterans in the complexities that everyday people are."
CBS' "NCIS" employs more than 100 veterans on the show's roster of 250, and Scott Williams, a writer and executive producer of the show, says the vets fully inform the stories "NCIS" produces. That means writing storylines with complex, multilayered individuals with leadership, experience and problem-solving know-how.
With some 200,000 servicemen and women leaving the military every year, highlighting that perception could make all the difference.
"It's more competitive to stay in," said Zachary Watson, who left the Marines in the fall. "So, now a lot of people are realizing, 'OK, I can't stay in here. I've got to get a job or something.'" Watson is taking advantage of the GI bill, enrolled as a full-time student. He believes a college degree will help him launch a successful career in TV or film but thinks his military experience would be the most valuable to future employers.
"At 22 years old, I was in charge of an entire crew, and I was responsible for being part of the whole organization and unit that was repairing helicopters that are [worth] millions of dollars. How many 22-year-olds are in charge of stuff like that?"
Experts urge companies to consider adapting their approach to recruiting veterans — anticipating unique needs for acclimation and retention — in a similar way that they've had to change their approach for hiring millennials. Veterans say those in the armed forces need to prepare themselves for the civilian world six to nine months before leaving the military, taking advantage of the tools available to them through the military, the Veterans Administration and support groups.
Martinez, who is taking a break from acting to study psychology full time at Fordham said, "As much as we're talking about hiring veterans and giving them an opportunity, we hope people don't translate that to just saying, 'Just hire us on the spot because we're veterans and because of what we've done for this country.' We want to be in the conversation. Give us a chance to sell ourselves to you, and to prove to you that we can, and we will!"
CNBC's Michael Newberg contributed to this report.