(CNN) -- The parents of a missing Missouri girl have refused to be interviewed separately by authorities, Kansas City police said Wednesday.
But the attorney representing Jeremy Irwin and Deborah Bradley, parents of 11-month-old Lisa Irwin, said the couple is not opposed to separate interviews, but do not want what police requested -- an unrestricted interview with no attorneys present.
"Being questioned separately is not the issue," said attorney Cyndy Short. She said the couple has been cooperative and has previously been interviewed separately as well as together. They don't mind being interviewed separately as long as the detectives are fair, open-minded and non-accusatory, she said.
Lisa was reported missing about 4 a.m. October 4, after her father, Jeremy Irwin, arrived home from work to find the door unlocked, the lights on and a window that had been tampered with. The girl's mother, Deborah Bradley, said she last saw Lisa at 6:40 p.m. the night before.
Kansas City police Capt. Steve Young said Tuesday investigators had planned to conduct the separate parent interviews, but said Wednesday the couple had declined. Young said he did not dispute reports that the family had cooperated and answered questions, but the police department detectives still had unanswered questions.
Meanwhile, Lisa's half-brothers, who were in the family's home the night she disappeared, will be re-interviewed by authorities on Friday, Kansas City police said Wednesday.
The boys will be interviewed by a "child services specialist trained to interview kids," Young said. The interview will be non-confrontational, he said, and a police officer won't even be in the room.
"Not an interrogation," he said. "They are kids, after all."
The boys are 8 and 6, Short said. Young said they were previously interviewed just after Lisa disappeared, both for under an hour.
Details were being worked out for a re-interview of the boys, Short said.
Bradley said in an NBC interview last week that she was drunk the night Lisa disappeared and that she had last seen the baby about four hours earlier than initially reported.
The couple said in the same interview they had refused to let authorities re-interview Lisa's older brothers.
"They said they heard noises (the night Lisa disappeared)," Bradley said. "I don't know if that was before we went to sleep or after." She said she had not talked to her sons about it because she was reluctant to put them through "anything else."
The couple's oldest son is Jeremy Irwin's, and their middle son is Bradley's son, Short told CNN in an interview Monday.
"Lisa was the little girl that was going to hold this family together," Short said, adding the child was wanted, looked forward to and "well-loved."
Asked about Bradley's admission that she was drinking the night Lisa vanished, Short said Bradley did what a lot of parents do when their children are in bed -- shared some drinks with a friend. "It's just not that unusual until your life gets turned upside down," she said.
Authorities had expressed frustration early in the investigation after Lisa's parents stopped cooperating with investigators, Young had said. However, a family spokeswoman attributed the frustration to "miscommunication," and meetings with the toddler's parents resumed shortly afterward.
A cadaver dog searching the family's Kansas City home indicated a positive "hit" for the scent of a body, according to documents released Friday.
On that information, Short said that law enforcement typically begins such investigations inside the home, then if warranted the probe moves outside the family. "We don't know exactly what happened here, so we need to keep broadening the investigation," she said, adding she is hopeful that the investigation is going in that direction.
Between 30 and 50 investigators, including police and FBI personnel, were involved in the search as of Tuesday, the Kansas City Police Department said. Some 900 tips had been received by investigators, the department said.
Surveillance video surfaced over the weekend from a BP gas station less than two miles from the family's home, showing an unidentified person walking along the road about 2:15 a.m. October 4. The station's manager, Anuj Arora, said it's unusual to see anyone walking at that time of night in the area.
On what Lisa's parents believe happened to their daughter, Short said, "They don't know. I mean, someone came into their home in the middle of the night and took their beloved child away from them ... They are stumped." She said the couple has provided a wealth of information to police, including the names of people who have had access to their home.
Lisa's parents want people to continue looking for the child, she said. "We are praying and hoping. Hope is alive for us."