Air Force Maj. Jill Metzger was due to return home Friday from her station oversees. Instead, she remains missing in Kyrgyzstan where she was last seen on Tuesday.
Officials in Kyrgyzstan said she was not kidnapped but the U.S. Air Force has not ruled out foul play.
Metzger, 33, disappeared after being separated from a group of servicemen while visiting a department store in Bishkek.
Jill's husband, Capt. Joshua Mayo, and his father, Kelly Mayo, spoke with CBS News Early Show co-anchor Julie Chen on Friday.
Joshua Mayo said he last spoke with his wife on Monday morning.
"We discussed a few family matters and then we discussed her trip going off the base and about her coming home and all of the things that we were looking forward to doing," Mayo said.
"I just told her to be safe," he said.
Kelly Mayo described his daughter-in-law as "just incredibly full of life, effervescent. This woman sees no evil in the world. There's good in everybody. She's incredibly trusting. She's a very innocent 30-year-old woman and she is really the light of our life."
Joshua Mayo said he does not plan to go to Kyrgyzstan to help in the search for his wife.
"We're going to stay here," he said. "I believe that my place is here with my family. ... I believe in our government to get things done to solve this case. I think there's about 20 highly skilled, highly trained, experienced agents over there right now rattling cages and looking for her. I believe that my efforts here would be better served honoring Jill's memory."
In Kyrgyzstan, Interior Ministry spokesman Nurdin Jangarayev told the Associated Press that Metzger and another U.S. servicewoman were recorded on a security camera on Tuesday afternoon as they entered the TsUM department store in central Bishkek. She separated from her companion three minutes later, he said.
In the next three hours, two calls were placed to her cell phone but neither was answered; records show that the phone was in the area of Bishkek's bus station when one call was placed, but was in another neighborhood for a later call, Jangarayev said.
"This is worrying because it could mean that her phone was in someone else's hands or that she was unconscious and could not reply," he said. The ministry, which oversees the police, is also trying to establish the holder of a phone she called about 45 minutes before she was last seen, he said.
Police Chief Moldomusa Kongantiyev said Wednesday that Metzger had been expected to return to the United States by the weekend.
A statement from base officials said group of 22 U.S. military investigators and logistics officers along with Kyrgyz police are involved in the search for Metzger, who was stationed at an air base near Bishkek with the 376th Air Expeditionary Wing.
She was dressed in civilian clothes at the time of the disappearance, according to base officials.
Capt. Anna Carpenter, a U.S. military spokeswoman in Kyrgyzstan, said "there has been a lot of progress" in the investigation but could not discuss details.
The Pentagon on Thursday formally declared Metzger missing, a status officially known as "duty status whereabouts unknown," and disclosed that her normal duty station is Moody Air Force Base, Ga., as a member of the 347th Mission Support Squadron. It said she was on temporary duty in Kyrgyzstan but offered no other details.
In 2003, Jill Metzger was stationed at Ramstein Air Force Base in Germany when she won the women's division of the U.S. Air Force Marathon, The Henderson Daily Dispatch reported at the time. She was a member of the Air Force-Europe team.
Metzger had run in every Air Force marathon since its inception seven years earlier, the newspaper said, and had run marathons in Paris, Amsterdam and Berlin.
Base officials announced new travel restrictions Thursday, barring all off-duty personnel from leaving the base until Metzger is found.
The U.S. military has maintained an air base at Kyrgyzstan's main civilian Manas airport since 2001, backing operations in nearby Afghanistan.