But it was never glamorous to his son and daughter, who have taken the names Gregg and Gina, and written a book, "On the Run," about their years in witness protection.
They say their lives were only made worse in witness protection, thanks to a harrowing existence created by their father, Correspondent Charlie Rose reports.
The real Henry Hill wasn't born into the mob. He was half-Italian and half-Irish, and he had to earn his way in. At a young age, he became obsessed with the idea of wise guys and gangsters.
"In my neighborhood, where I came from in Brooklyn, these were the guys with the silk suits and the diamond rings and the beautiful women," says Hill.
Hill did everything he could to make it into organized crime. For 20 years, he lived the mob life, until May 1980, when it all came to a crashing halt.
Hill was arrested on drug charges and faced serious jail time. The government offered him a deal. If he testified against fellow mobsters, the charges would be dropped and he would be protected.
"I was in trouble. I knew I was a dead man, no matter how you cut it. If I stayed in prison, I was dead," says Hill. "Went out in the street, I was dead. So, I mean, my choice was already made."
Gregg was 13 and Gina was just 11 when their father made their deal with the government. Although they are out of the program now, they insisted that 60 Minutes disguise them. They say only their spouses know who their father is, and what he used to do.
"He was what, in mob parlance, they called an earner," says Gregg. "He had scams, from gambling, extortion, arson that brought money to the mob."
Gregg and Gina have limited contact with their father today. Growing up, they had tried hard to ignore his criminal activities, no matter how obvious.
"We tried our best to ignore it, and live our separate lives and do things that normal kids do," says Gregg.
But any chance of being normal kids ended the day the family entered witness protection and were told they had to leave their home on New York's Long Island.
"I'm very angry," says Gregg. "Up until that time, all my father's exploits really only affect him. This was the first time we started feeling the impact of what he was doing. And to be told we were leaving forever. It was a hard fact to sink in."
It happened literally overnight. Gregg and Gina had to pack as much as they could into plastic garbage bags, and then were taken away.
Hill, who also has a book out, offers no apologies. "They'd have locked my kids in a refrigerator if I had left them behind, to get me back there," he says. "My friends."
The government first hid the family in Omaha, Neb., land of rolling cornfields, fresh air and great open spaces. They were given $1,500 a month, and a house to rent. But Gregg and Gina felt a million miles from home.
"I thought we stood out like a sore thumb. My father had jet black hair. Thick Brooklyn accent. My mother had jet black hair. Thick accent," says Gregg. "And the first place we go is Godfather's Pizza. True story. The irony was there."
And while the witness protection program was good at hiding people, it didn't help at all with an alibi. The family was on its own to re-invent their past, right down to choosing a new last name.
"The only thing they told us was, 'Don't tell anyone you're from New York,'" says Gregg. "We used the cover story that my mother and sister came up with -- that my father worked for the government."
Hill was working for the government. He was testifying against his old mob partners. He says his testimony sent about 50 people to jail. "I was scared to death at the time," he says. "But I was telling the truth."
Back in New York, there was a half-million dollar price on Hill's head, but the mob death sentence had no apparent impact on their father.
"He just refused to make any kind of effort to change," says Gina.
"He made calls to his drug-dealing friends. He made calls to his girlfriends in New York," adds Gregg.
The information made its way back to Jimmy Burke, the man who put the bounty on Hill. In the movie, "Goodfellas," Robert De Niro plays Burke, a cold-blooded killer. In real life, Hill's testimony put Burke behind bars, and Burke was heard in court telling associates to get him.
"They overheard him say, 'I know that guy's in the Midwest,'" recalls Gregg. "That was enough to spook the Feds to call us and say, 'We'll pick you up tomorrow morning.'"
After just two months in Omaha, the Hills were on the move again: changing their names and re-inventing their past once more. Their next stop was Independence, Ky., surrounded by tobacco fields and horses. The population: 8,000.
Gregg says it was a culture shock: "My father, oddly enough, was the one who probably adapted better than any of us. He had the cowboy hat and the Willie Nelson playing soon after we arrived."
According to Gregg and Gina, Hill spent his days at the racetrack gambling, and his nights drinking.
"I wanted him to get a job. I didn't care what it was, I wanted him to get a job," says Gregg. "That's all I ever asked [for him to be a normal father.] That's all I ever wanted."
In Kentucky, Hill found a way to supplement his monthly stipend. He co-wrote a blockbuster article in Sports Illustrated about his role in a point-shaving scheme at Boston College.
Gregg says the FBI went nuts and "threatened to throw him out of the program." But the FBI still needed his testimony. His safety, however, was compromised, and after about a year in Independence, the Hills were uprooted once again.
The family was taken this time to Redmond, Wash., a city east of Seattle. In Redmond, their father had run-ins with the local police and was arrested several times for drunk driving. Gregg and Henry got into frequent fights.
One day, when he was 19, Gregg couldn't take it any more. "One of the most painful things I ever did was leave my mother and my sister. But I knew if I stayed there, something terrible would have happened," says Gregg.
Gina says it was very hard for her. "It ended in a very bad physical fight between my brother and my father," she says. "I didn't know that my brother had left town. I thought I'd see him after a couple of days when things died down, like they always did. And he never came back."
Gina says her mother "cried as hard as I did." Her father, however, didn't "shed a tear." She says she "never bothered to ask him."
Hill says he wasn't angry, but he was sad. "I couldn't believe that I had forced my son to leave," says Hill. "It was my fault he left."
To this day, Gregg and Gina say they rarely talk to their father. Rose played some of their interview for Hill.
"Amends take a long time. Sometimes it never happens," says Hill.
It remains to be seen if those amends will ever be made. But Gregg and Gina aren't waiting for the call. Was any part of their book written in revenge?
"None of it. All this book is for more than 20 years, we've lived with him telling our story," says Gregg. "With others telling our story. This book is our story, on our terms, in our voice."