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.