When Christopher Reeve’s children, Matthew, Alexandra and Will Reeve, were little, their father – who became a worldwide sensation after being cast in the 1978 film – Superman — was the type of man who could do absolutely anything: fly airplanes, sail yachts, ski, skate, ride horses, play the piano.

He was also very smart, having studied at Cornell and Juilliard. But as much as he seemed like a true hero, it was the way he handled his life after his fall from a horse in 1995, which left him paralyzed from the neck down, that had the greatest impact on his children.

“Heroism is so much more than superficial strength and a glossy image,” his son Will, 32, tells PEOPLE of his father’s legacy. “It’s about integrity, standing up for your family, persevering through difficult circumstances and still having that joy in life. That was our dad.”

The actor’s three children are excited to share a glimpse into their father’s private life in the new documentary, both before and after the accident Super/Man: The Christopher Reeve Story (produced by Words + Pictures), opening in select theaters only on September 21 and again on September 25 (the day Reeve would have turned 72).

While the film impressively shows how Reeve coped with adversity and developed into an activist for the paralyzed community, it does not overlook Reeve’s life before the accident.

He was indeed famous and handsome, but he also had problems, including a troubled relationship with his father, a strict professor he could never please, and inner turmoil over being pigeonholed as Superman.

He also left his relationship with Matthew and Alexandra’s mother, British modeling agent Gae Exton, when the children were young, leaving her heartbroken. The film helped the children better understand their father.

“It’s beautiful to be able to see the full picture of someone’s life,” said his daughter Alexandra Reeve Givens, 40, an activist who serves on the board of the Christopher & Dana Reeve Foundation.

She adds: “There were highs and lows, but also two deep, true loves and (three) children that merged together into this beautiful family.”

Matthew, Reeve’s 44-year-old eldest son, is a filmmaker whose footage from two previous documentaries he made about his father is used in the new film. He also says they wanted to tell the full story of his father’s life.

“We wanted to honor his story but not sugarcoat it,” he says, noting that it was also important to show how difficult Reeves’ life was after the accident, from learning how to breathe on his own without a ventilator to the cost and physical toll it took on the actor and his caregivers, including his devoted wife Dana, who devoted herself to caring for her husband.

Will, who was almost 3 when his father was injured, says of Dana Reeve, “My mother was perhaps the most extraordinary person who ever walked the earth. She had a unique combination of grace, beauty, compassion, courage and intelligence.” All three children agree that Dana was the glue that held the family together after the accident.

The film’s directors, Ian Bonhôte and Peter Ettedgui, say that while making the film they discovered how much Reeve changed, not just physically but mentally, as a result of the injury.

“Christopher learned what was important after that,” Bonhôte says. “It wasn’t about making a successful film or getting more roles. It was about his family and focusing on his close ties.”

Alexandra says, “Our father had a near-death experience, so he knew not to leave anything unsaid. Because we were suddenly not doing any physical activities, we had a lot more time to sit and have conversations in his office. That was a real gift.”

Will added: “I see Matthew and Alex being phenomenal parents … with my mom and dad shining through in the best way. You’re there for the people you love and you give them everything you’ve got because you don’t know how long you’re going to have with them. That’s something I’ve taken from my childhood and I’ll carry with me for the rest of my life.”

For tickets to see Super/Man: The Christopher Reeve Story, visit Fathom Events.

Want to read more about Christopher Reeve’s extraordinary life? Pick up the latest issue of PEOPLE, in stores Friday.