"The U.S. government could have done a lot more"

Matthew and Grace Huang are home in Los Angeles. Their return comes after a nearly two-year legal battle to win their freedom from a Qatari prison. The couple was cleared in the death of their eight-year-old daughter, but they still don't know what killed her, and it's clear healing will take time. Margaret Brennan sat down with the couple for a "CBS This Morning" exclusive interview.

"We're so excited to be home," Matthew said.

The couple are just beginning to piece their life back together. It started Sunday with a rousing welcome home at their Pasadena church, which made the deeply faithful Evangelical couple feel at home.

"It was just nice to be there with our church family again," Grace said.

They've reunited with their two sons, Emanuel and Josiah, both adopted from Africa.

But the fate of their third adopted child, Gloria, is haunting them.

U.S. couple held in Qatar despite acquittal in adopted daughter's death

"But at the same time, we were just sitting in our usual order with the kids in between us, but there was just one who was missing," Grace said.

While living in Qatar, where Matthew was working as an engineer with an American firm, their eight-year-old girl died suddenly and mysteriously.

"Gloria was on the floor, foaming at the mouth, so I took her immediately to the emergency room at the hospital," Matthew said. "They did about 40 minutes of CPR and then they told me that Gloria had passed away."

Gloria suffered severe malnourishment as a small child in Ghana and continued to have eating disorders, despite her parents' best efforts. She refused to eat for the final four days of her life.

Qatari police accused Matt and Grace of starving her to death and prosecutors were suspicious of a mixed-race family, an uncommon sight in Qatar.

"They thought we were human traffickers. They said we adopted our children to either harvest their organs or to do medical tests on them," Matthew said. "I mean, this is an outrageous charge against us-- who's a loving family. But the Qatari authorities just didn't understand multi-ethnic adoption."

On Grace's part, it was difficult having to constantly address that she was Gloria's adopted mother.

"For me, the hardest part, I think, was being asked over and over, 'Are you the real mom?'" said Grace, adding she was told "you're not the real mom because you're different colors."

One day after Gloria's death, the Huangs were thrown in a Qatari prison and Josiah and Emanuel were sent to a Qatari orphanage.

"It was scary to be in prison," Grace said. "And it was scary to have our sons in a place where we just didn't know how they were being taken care of."

Prison was especially difficult for Matthew.

"I was physically and sexually assaulted," Matthew said. "Another inmate tried to rape me."

"I-- as-- as a victim, I fought back," he said.

As a mother, confronting the reality of her children's fate was no easy task.

"I was angry with myself. Like, what could I have done to keep them from taking the kids away?" Grace said.

After nearly a year behind bars, a judge granted them bail as discrepancies in the prosecution's case began to surface.

A forensic pathologist hired by the family concluded there was "no medical evidence that Gloria's parents starved her" and said the Qataris never performed a proper autopsy.

"They didn't take any tissue samples," Matthew said.

"They even got her height and weight wrong on the autopsy," Grace said.

Matthew believes that the Qatari Attorney General was personally involved and unwilling to admit that mistakes had been made in the case.

While their appeal dragged on, Matthew Huang lost his job. They were banned from traveling and rarely left their home.

While the U.S. State Department publicly called the Huangs trial "unfair" and privately plead for the release, Matthew questioned whether political interests kept American diplomats from lobbying Qatar for their release.

"The U.S. government could have done a lot more, a lot quicker," he said. "Qatar is such an important military base -- for the U.S. I felt like the U.S. government was unwilling to rock the boat and unwilling to make a strong stance with knowing that we were innocent."

A Senior State Department official disputed that characterization and said that Secretary Kerry personally raised the issue several times with both Qatar's Foreign Minister and Emir "several times" over the past year. Qatari officials declined to comment.

Suddenly last Sunday, a Qatari judge overturned their conviction, citing the inadequate autopsy and described the Huangs as caring parents.

"I'm so excited that truth prevailed," Matthew said.

The elated mom and dad documented the long trip home and now are trying to catch up on the life they missed.

In another legal battle that begins Monday, Matthew is suing his employer in Qatar, saying they never adequately represented him.

"We had no clue that race would be a factor when we moved to Qatar," he said. "We did not have a clue about the racism in Qatar. We did not have a clue about the judicial system and how poorly it's run."