(CNN) -- When Elizabeth Joice found out that she was pregnant, she and her husband, Max, were ecstatic.
A fertility specialist had told her that this would never happen, Max says, because of the chemotherapy Elizabeth underwent to beat sarcoma in 2010.
"It very much felt like a miracle," he says. "Bringing a child into this world -- I mean, it wasn't just important for me; it was one of the most important things for Liz."
Then, one month into her pregnancy, Elizabeth's cancer returned, he says.
Surgeons removed the tumors in her back, but she needed a full-body MRI scan to know whether the cancer had spread. Because an MRI's contrast dyes may damage a developing fetus, she faced a difficult decision. She could either terminate her pregnancy to undergo the scan or continue with the pregnancy without knowing her true cancer status.
"We felt that if we terminated this pregnancy and did these scans, if it turned out that there was no evidence of this disease after the scans, then we would have possibly given up our only chance at having a child naturally and would have done it for nothing," Max said.
"It was a calculated risk. We knew there was a possibility of a worst-case scenario, but we also thought there was a good chance that we could have the baby."
Shortly after becoming pregnant, Elizabeth was introduced to filmmaker Christopher Henze. His upcoming documentary on pregnancy and motherhood will include the Joices' story.
"It took about three minutes to realize that Liz was a stellar human being, and I wanted her for my movie," Henze said. "I was impressed by the way she looked at cancer as another problem to be solved."
Even though a shielded chest X-ray taken in November found no sign of cancer, by January, she was having trouble breathing. Another X-ray revealed tumors in her lungs. Her C-section date was moved up, and on January 23 -- six weeks early -- Lily Joice was born.
"It was incredibly difficult to want to enjoy this amazing moment as much as you possibly can," Max said. "Yet to know that you're facing something so incredibly dire, and the chances didn't look good at that point."
After delivery, doctors found cancer in Elizabeth's heart, abdomen and pelvis.
She died in the hospital on March 9. She was 36.
"In the face of this life-threatening illness," her husband said, "she was so optimistic and so strong and so willing to go through whatever fight she would have to go through in order to have this baby."
Henze delivered a eulogy at Elizabeth's funeral.
"Lots of people say 'Liz was'; I say 'Liz is,' " Henze said. "Through her spirit and grace, she is still affecting people, and she will through the movie, will continue to impact people. Liz is."
CNN's Jennifer Bixler contributed to this report.