Barry and Marybeth Mosier were on their way to visit their son Keith, 24, in Kinsangani, Congo, with two younger children when their plane crashed on takeoff Tuesday in Goma. At least 36 people died as the plane plowed through a market and burned. Most of the people who died were on the ground, according to the U.N. mission in DR Congo.

April Mosier, 14, managed to escape quickly, her father said from Goma.

"April raced ahead, and she got to the front of the plane as one of the first people, I think," said Barry Mosier, 53.

The girl encountered a man who was tearing through an opening in the fuselage, Mosier said.

"He was pulling parts of the plane in or pushing them out, trying to make a hole. And she told him -- she speaks Swahili well -- she said, 'We've got to get a hole in this plane, or we're all going to die.' " Watch as Barry Mosier describes the chaos »

When the hole was big enough, April tried to dive through it. She made it with a push from the man, and other passengers followed, he said.

Meanwhile, Mosier said, he and his wife were carrying their son Andrew, 3, in the shoving "mass of humanity" trying to escape the burning plane. They got out through the opening in the fuselage. The child's leg was broken in the crush of people, but his parents didn't realize it until later.

April became separated from her parents and was whisked away to a hospital, convinced that her family was dead, her father said.

"Outside the plane, she was wandering around. ... It was total chaos," he said. "People were screaming and yelling because the plane had landed on this market. All of a sudden, out of the blue, all of these people who were just standing there are now dead.

"So there's parts of bodies and people burning and people screaming and yelling, and she was out there by herself."

About 25 minutes later, the Mosiers were reunited at the hospital.

"When we saw each other at the hospital, I can tell you, it was a grand reunion," he said.

The Mosiers, who have been Seventh-day Adventist missionaries in Iringa, Tanzania, for eight years, went to the church office in Goma to let Keith and other loved ones -- including two other grown children in the U.S. -- know that they were all right.

While there, someone noticed that Andrew's leg was swollen, and the Mosiers returned to the hospital. They learned that Andrew's femur was broken near the hip, and he is now in a cast that reaches from his toes to his rib cage, Barry Mosier said.

"He doesn't like it very well, as most 3-year-olds wouldn't," Mosier said.

The family will recuperate in Goma for a few days before deciding whether to resume the trip to Kisangani, where Keith Mosier has been a volunteer missionary for two months, Barry Mosier said.

"But flying here is not a popular thing to talk about just now," he said wryly.

Andrew has made up his mind, his father said.

"He says he doesn't want to ride in airplanes anymore," he said.

Marybeth Mosier, 51, suffered a black eye and bruised ribs, said her husband, who added that he was unhurt.

"We couldn't believe that our family of four could all escape a plane that was crashed and on fire, but by God's mercy, we did," he said.

Mosier said he believes the family made it for a reason.

"I think the Lord has a plan for us, otherwise we wouldn't have survived," he said. "He still has work for us to do."

And that work just might be in the Democratic Republic of the Congo.

Plane crashes into African marketplace

Antoine Ghonda, a Congolese lawmaker and former foreign minister, said the crash killed at least 18 people while roughly 66 others -- including five crew members -- survived. Those numbers from Ghonda, who is in touch with Congolese Interior Ministry officials, are down sharply from earlier estimates that as many as 75 were dead.

It was unclear whether those estimates included people on the ground.

"I can see shops that have been just completely destroyed," said Anna Ridout of relief agency World Vision, who arrived at the scene from her nearby office moments after the crash. "This was a market area where women were selling their goods. ... People were talking of people just being plowed over by the plane moving across the ground and through the shops and through wooden houses."

Ridout said the plane was "complete rubble" from the cockpit to windows beside the fifth row of seats. She said she expects casualties will be reported from the plane and among those at what she called a very busy market.

"I saw a lot of bodies being carried on stretchers," she said. "Also, we have photographs of figures who are unrecognizable in the wreckage. I would expect that, now that they're clearing the wreckage, that by tomorrow that number [of deaths] will rise."

Among the passengers who survived were members of an American missionary family from southeastern Minnesota -- Barry and Marybeth Mosier, and their children April and Andrew.

"It was horrible, fighting our way through the smoke," Barry Mosier said in a phone interview with CNN affiliate KTTC of Rochester, Minnesota. "We couldn't see. We saw flames, especially back toward the wings where the fuel was."

The Mosier's 3-year-old son, Andrew, broke his leg while being pulled out of the wreckage, but 13-year-old April and her parents are only nursing minor bumps and bruises, according to KTTC.

"We were just trying to get out," Barry Mosier said. "My wife grabbed a man who was stuck under a seat but she could not pull him out. There were others crying for help but we just couldn't see very well, and we knew we had to get out of the plane."

According to a manifest obtained by the U.S. Embassy, there were 79 passengers and five crew members aboard the plane.

The final death toll is unclear as rescue workers continue to search the burned wreckage of the DC-9 passenger jet.

A journalist who witnessed the aftermath described "a scene of total devastation and chaos." Watch iReport video of crash aftermath »

Journalist Mick Davie said a crowd gathered "to try to either put out the fire ... or loot what remained of the aircraft."

"Only the very tip of the nose cone and the tail of the airplane were intact," he said. "There was a huge amount of debris -- the roofs of maybe a dozen buildings in the immediate vicinity had been taken off [by the plane]."

He said the plane "didn't actually make it into the air because the runway here in Goma is a little higher than the rest of the town."

The runway was shortened five years ago after a volcano erupted and destroyed nearly half the town.

The flight was heading from the eastern city of Goma to the central city of Kisangani, Ghonda said. He said the cause of the crash is believed to be engine failure.

The plane went down shortly after 3 p.m. (9 a.m. ET) and was still on fire several hours later, Ridout said.

The United Nations and the Red Cross were helping with the rescue effort, which was being hampered by the "very basic, if nonexistent" rescue equipment in the impoverished country, U.N. spokesman Kemal Saiki said.

Those who helped pull people from the burning wreckage said the survivors include the pilot, the co-pilot and a baby, Saiki and Ridout said.