“I remember during the Gulf War, my father’s ship had just finished a deployment in in the Gulf and was on its way back when the war started in Kuwait,” Murray, 39, tells PEOPLE. “They turned around and went back to the Gulf. I have this memory of being at home and watching Saddam Hussein on the television. He was saying that the rivers would run red with the blood of American soldiers. That was when everything hit me with what my dad does.”
Growing up as a Navy brat meant Murray bounced around between bases and spent long stretches of time away from his father. But he also had opportunities that non-military kids didn’t, like going on Tiger Cruises, which allow sailors to invite loved ones to experience life on a Navy ship.
“Spending a week aboard an aircraft carrier as a 10-year-old was pretty wild,” says the Hocus Pocus alum, who flew to Hawaii to return to the port in Naval Air Station Alameda outside of San Francisco with his dad. “I wandered into the war room — I’m still not exactly sure what that is, but apparently it’s not a place that a 10-year-old should be. I remember them paging my dad to have him come get me out of the war room.”
Though Murray never considered following in his father’s footsteps by enlisting, he was able to incorporate a piece of their relationship into his NCIS gig.
“Early on in the series, we were going to be in McGee’s apartment. Some quick decisions were made as far as what kind of pictures will we have and they said, ‘What about a picture of you and your father?’ ” he recalls. “So there’s a picture of me and my real father together in McGhee’s apartment set, which is kind of cool and sort of inspired the rest of the character’s story.”
The Maryland-born star says his dad “loves the show,” adding, “I’m pretty sure he would watch it whether I was on it or not.”
Murray and his character both come from military families and have spent time on the Norfolk Naval Station in Virginia. He was able to connect with others who’ve had similar experiences when the cast recently visited the USO San Diego to provide support and raise morale.
“It was really awesome. Getting to see all the service people and their families,” Murray says. “Doing something like that is kind of a no-brainer.”
Though Murray says his dad, now a retired Navy Captain, likes to downplay his time in the service, they acknowledge Veterans Day by catching up over a long phone call. “It’s like tossing a baseball back and forth with your dad,” the JAG vet says.
And for those without a serviceperson in their lives, they can still connect with military members they encounter in daily life. “Just thanking someone for their service alone is a great thing you can do,” Murray explains. “We’ve got one day a year [when] people hopefully think about and pay their respects and acknowledge service people. These people are heroes. I hope that on Veterans Day people think about those who protect us from the evils out there.”
NCIS airs Tuesdays on CBS at 8 p.m. ET.
This article originally appeared on PEOPLE.