(CNN) A missing Connecticut woman's blood was found mixed with her estranged husband's DNA in her kitchen, a prosecutor alleged publicly for the first time in court Tuesday during deliberations over the husband's bond.

The husband, Fotis Dulos, eventually was released on $500,000 bond Tuesday after he and his girlfriend pleaded not guilty to charges relating to the disappearance of his estranged wife , Jennifer Dulos.

On Wednesday, away from custody for the first morning in nearly two weeks, Fotis Dulos went jogging around Farmington, Connecticut, where he lives, CNN affiliate WFSB reported . Wearing a ballcap and headphones, he waved as a reporter approached in a vehicle, but he did not respond to a request for comment, the Hartford TV station reported.

The search for Jennifer Dulos continued Wednesday, with the Connecticut State Police dive team again searching a pond in Avon, north of Farmington, CNN affiliate WTIC reported

Fotis Dulos and Michelle Troconis were arrested June 1 and charged with tampering with or fabricating physical evidence and hindering prosecution in relation to Jennifer Dulos' May 24 disappearance.

State's Attorney Richard J. Colangelo argued for a higher bond -- $850,000 -- for Fotis Dulos, citing what he said was investigators' discovery of the man's DNA in a mixture of Jennifer Dulos' blood in a faucet inside her New Canaan home. Jennifer Dulos lived at that home with the couple's five children after she split from her husband in 2017.

But Superior Court Judge John F. Blawie denied prosecutors' request and kept the bond at $500,000, which Fotis Dulos eventually posted.

Jennifer Dulos, 50, was last seen driving a 2017 Chevrolet Suburban on May 24 in New Canaan, police said. Her friends reported her missing after she missed appointments and they hadn't heard from her in 10 hours. Authorities found her car near a park, not far from her house.

Fotis Dulos' attorney, Norm Pattis, said his client had no motive to harm his wife. Dulos faces financial problems and does not pose a flight risk, his attorney argued.

Troconis said through her attorney, Andrew Bowman, that she wants a jury trial. She was released on a $500,000 bail after her arraignment last week and is slated to be back in court July 18.

Blawie ordered her not to leave Connecticut without the court's approval.

Family asks for help finding mother of 5

Also Tuesday, relatives and friends of Jennifer Dulos asked the public not to lose sight of her case. In a statement, they asked for any information about her disappearance or whereabouts.

Jennifer Dulos, a mother of five, was last seen May 24.

"We must not lose sight of the enormous human cost of this tragedy: five young children have not seen their mother in 18 days. Jennifer is the constant presence in their lives. She has sole physical custody and has devoted her full energies to their care and happiness," her family said in a statement.

"Jennifer's family, friends, and above all her children are living in limbo -- missing her embrace, her lilting laugh, her bedtime backrubs, her gentle strength. Please know that the children are safe and loved and supported in every respect. But more than anything in the world, they long to know where their mother is."

Lawyer chides media

Outside the courtroom Tuesday, Bowman, Troconis' attorney, chastised journalists for what he said was "unfair and inaccurate" reporting, including statements that have been falsely attributed to him.

"I don't need to remind you that Michelle Troconis is presumed innocent," he said, "and when you put inaccurate information in the electronic and print media, it prejudices her right to a fair trial. I assume that none of us want to do that, so I would appreciate it if some of you could verify the reporting that you put in the paper."

Pattis told the judge: "We don't know where Jennifer is. We don't think the state knows where Jennifer is. We think that these bonds and these arrests were an attempt to pit the two of them -- Ms. Troconis and Mr. Dulos -- against each other in a classic prisoners' dilemma that was designed to give the first person to speak a 'get out of jail card' on charges that are flimsy on the outset."

As conditions of his release, Fotis Dulos will have to give up his passport, remain in Connecticut and submit to GPS monitoring, court documents said.

"We deny the charges," Pattis told reporters after the hearing. "We are resolute and determined to try this case, and we believe fully that our client will be exonerated. I would ask everyone to put aside the easy narrative here: that an angry ex-spouse took matters into his own hands to resolve a custody dispute. That didn't happen."

Heated custody battle

Jennifer and Fotis Dulos have been embroiled in a custody battle since 2017, and Jennifer Dulos has accused her husband of having revenge fantasies, exhibiting "irrational, unsafe, bullying, threatening and controlling behavior" and saying he would abscond with their five children to another country, according to her custody petition. She also said he owned a gun.

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Jennifer Dulos lived in a mansion in Farmington with her husband and family until two years ago. In court documents, she said Fotis Dulos moved his girlfriend and the woman's daughter into their house, and Jennifer Dulos moved out in 2017 to a home in New Canaan and filed for divorce, court records show.

Before her disappearance, Jennifer Dulos had told officials she was afraid of Fotis Dulos and feared that filing for divorce would enrage him, court documents indicate.

Fotis Dulos denied making any threats or bullying her, according to court filings.

Since their mother went missing, the Dulos children, aged 8 to 13, have been living with their maternal grandmother at her New York City apartment, according to court documents.

The evidence

Investigators looking into the woman's disappearance discovered stains that tested positive for human blood on her garage floor as well as evidence of attempts to clean up the scene of what investigators concluded was "a serious physical assault ... and Jennifer Dulos was the suspected victim," arrest warrants said.

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The day she went missing, surveillance cameras captured someone matching the description of her estranged husband getting out of his truck and putting "multiple garbage bags into various trash receptacles" in the Hartford area, authorities said. Detectives later recovered clothing and household goods from trash receptacles with Jennifer Dulos' blood on it.

Fotis Dulos is president and CEO of the Fore Group, a Farmington company that builds custom homes.

Police have obtained and served search warrants on his properties, according to a news release from New Canaan police spokesman Lt. Jason Ferraro.

"Details regarding these searches will not be released as it could compromise this very active criminal investigation," it said.