They said I failed (a polygraph test)," Bradley, 25, told the Associated Press. "And I continued to say that's not possible because I don't know where she's at and I did not do this."
Kansas City police spokesman Steve Young has declined to comment on any polygraph tests, citing the ongoing investigation.
Lisa's father, Jeremy Irwin, 28, says he has offered to take a lie detector test, but that police say that's not necessary.
Bradley and Irwin, both dressed in jeans and sweatshirts, held hands and teared up several times during the 20-minute interview. They reiterated that their main focus "is to bring Lisa home."
"We need her. We have to have her. She's our link that ties everybody together," Irwin said.
The couple said police have treated them like suspects and that Bradley in particular has been preparing for the possibility of charges being filed against her.
The mother said detectives told her: "'You did it. You did it. And we have nothing.'"
Irwin, an electrician, says he returned from work around 4 a.m. Tuesday and discovered Lisa was missing. Bradley says she last checked on the child around 10:30 p.m. and that when Lisa disappeared she was asleep in her bed with her 6-year-old son and a stray kitten they found earlier in the day.
The parents say they discovered their front door unlocked, a window open and house lights blazing, lending credence to the theory that the baby may have been snatched by an intruder.
"The main problem I think that we're facing is that everybody (else) has an alibi," Irwin said.
"I was at work. I've been cleared. All these other people we were worried about ... the FBI said they've been cleared.
The only one you can't clear is the mother that's at home when it happens `cause there's nobody else there."
On Thursday, police told reporters that Bradley and Irwin were no longer cooperating with authorities in their investigations, but the family later released a statement insisting they had never stopped.
The parents reasserted their commitment to the investigation Friday, saying they are not angry with how things have gone and that they understand police have a difficult job to do.
"Don't get me wrong. I understand why they did what they did," Bradley said. "You see stuff like this everywhere. You watch the TV, and there's some crazy person doing something insane.
There's been too many times stuff has happened.
They have to assume what's worst ... but it felt like it was taken really, really far."
Bradley said, "I'm still not angry."
Earlier Thursday, up to 100 officers conducted a shoulder-to-shoulder search in a wooded area near the couple's home. The girl's parents were later seen having an "animated discussion" with detectives working the case, WDAF reports.
Police said Bradley and Irwin claim three cellphones were also taken from their home.
Sources also told the station that a phone call was made from the couple's home at about 2:30 a.m. Tuesday.
"They told us that that morning. What the detectives have done with that I don't know," Young on Thursday.
"Clearly it hasn't led to a big break in the case or I'd probably be able to talk about it. I can't get into details of what we're doing, but it's safe to say we're leaving no stone unturned."
In a statement to media outlets Thursday, Irwin's sister disputed claims by police that the couple had stopped cooperating with detectives.
"We want the public to know we have never stopped cooperating with police," the statement read. Irwin's sister said the couple plans on releasing their own statement on Friday.
Authorities announced late Thursday that they were shutting down the command post about a mile from the family home. Police spokesman Darin Snapp sent out a news release saying authorities believed they had done everything they could "regarding geographic searches."
Lisa has blue eyes and blonde hair, is 30 inches tall and weighs around 28 pounds. She was last seen wearing purple shorts and a purple shirt with pictures of white kittens.
The Associated Press contributed to this report.
