They're among a group of wounded warriors on the front lines of a suicide crisis.
In this multi-part documentary series, Logan investigated the state of America's veterans through their own stories.
She met Martinez and Jackson on a beach in La Jolla, Calif. the day before they were set to compete in the 2020 World Para Surfing Championship.
"About eight years ago to the day, I actually stepped on the 60-pound I.E.D that was meant for a vehicle," said Martinez matter-of-factly. "They told my unit that I was dead instantly.
"My boys jumped on top of me. They saved my life," he remembered with a smile. "I woke up 10 days later from the coma, scaring the doctor."
Martinez lost both legs, his right arm, the index finger on his left hand, and some internal organs. His right leg was amputated to the hip joint, in a rare procedure called hip disarticulation.
Jackson, like so many other veterans of the wars in Iraq and Afghanistan, is burdened by another type of injury: post-traumatic stress disorder.
"I came back to surfing after Iraq," he told Logan. "Surfing kept me alive."
"I would literally be having a bad night," Jackson continued, "I would just sleep on the beach til I could get up in the morning and go surf. And I felt that if I still felt the way I did before surfing afterwards [then] I knew how I felt -- which meant committing suicide.
"I felt miserable... I felt I was complaining compared to people like these folks," he said gesturing to the other wounded veterans on the beach.
"Like that you had no right to be depressed," Logan suggested.
"Because it's all in my head," said Jackson, nodding in agreement.
Jackson carries Martinez's board into the water and helps him catch the waves. He's also there to grab Martinez if he falls off his board.
In return, Martinez is a calming presence for Jackson, though he jokingly admits that their relationship was something they had to work on.
"It looked like he wanted to kill me sometimes because I need help to get pushed into the wave," said Martinez. "It's been awesome trying to figure ourselves out."
Martinez and Jackson work together as a team, but they are also surrounded by a community, just as they were in the military.
One More Wave is a nonprofit charity started and run by a group of former Navy SEALs. They build surfboards specially designed to accommodate the needs of specific wounded veterans.
Martinez's board is equipped with a handle. He lies on his stomach and uses his body weight to steer.
"We thought that gear was going to be the cool thing... but that's not it at all," said Rob Garnett, chief of operations for One More Wave. "It's us going out as a group and forming community and getting in the water with other vets and surfing and kind of sharing. That's where the magic is."
To watch more of this episode and more of "Lara Logan Has No Agenda," and meet the veteran turned documentary filmmaker, who is also telling the story of the suicide crisis, go to Fox Nation and sign up today.