HUDSON, Wis. — A jury on Tuesday rejected an insanity defense by a Wisconsin father who admitted to killing his three young daughters last July, finding he had a mental defect but still understood he was doing something wrong when he slashed his girls’ throats, then tucked their bodies into bed.

Aaron Schaffhausen, 35, faces a maximum penalty of life in prison with no parole when he is sentenced. The St. Croix County Circuit Court jury deliberated for about 3 1/2 hours before reaching its unanimous verdict.

Schaffhausen pleaded guilty earlier to three counts of first-degree intentional homicide and one count of attempted arson. But he maintained he wasn’t responsible for killing 11-year-old Amara, 8-year-old Sophie and 5-year-old Cecilia because of a mental illness.

The jury was tasked with weighing Schaffhausen’s sanity. Prosecutor Gary Freyberg said jurors found “the truth of the case.”

“He was guilty. He was sane. And the jury got it right,” Freyberg said. He called the killings a “brutal, brutal series of crimes” and added: “He understood what he was doing. He said he was going to do this, and he went out and did it.”

Flint Watt, an uncle of Schaffhausen’s ex-wife Jessica, said the family views the verdict as one step in a long recovery.

“Aaron’s going to be spending a long time, I think, thinking about what he’s done,” Watt said. Some of Jessica’s family members sighed and quietly cried as the verdict was read.

Defense attorney John Kucinski said he would appeal. He said Judge Howard Cameron instructed the jury on motive when it wasn’t relevant. He also said the judge shouldn’t have denied the jury’s request to have expert reports in the room as they deliberated.

“I don’t think the pieces fit with the finding,” Kucinski said of the verdict. He said Schaffhausen was depressed by the decision.

Each murder count carries a mandatory term of life in prison, but Wisconsin law allows for parole after 20 years. Judges may also make sentences consecutive or concurrent. That means Schaffhausen faces a minimum of 20 years in prison and a maximum of life in prison without release.

Evidence showed that Schaffhausen texted his ex-wife July 10 to ask for an unscheduled visit with the girls. She consented but said he had to be gone before she got home because she didn’t want to see him. The girls’ baby sitter told investigators the children were excited when he arrived. The baby sitter left. He called his wife about two hours later, saying: “You can come home now, I killed the kids.”

Police arrived to find the girls lying in their beds, their throats slit and their blankets pulled up to their necks. White T-shirts were tied around their necks. Cecilia’s body also showed signs of strangulation.

In his closing argument Tuesday, Freyberg told jurors Schaffhausen was a manipulator who knew what he was doing and wanted to punish his ex-wife in the worst way imaginable.

“These children did not have to die. They died because their father made a choice,” Freyberg said. “He chose to kill them and betray everything that a parent stands for because he was jealous and angry.”

Kucinski argued Schaffhausen has a rare mental disorder, rooted in a deep dependency on his ex-wife. Kucinski said the only way Schaffhausen believed he could “solve” that problem was to commit suicide or homicide. He said a mental disease is the only way to explain how Schaffhausen could kill the girls he loved.

“There is nobody involved in this case that deserves an iota of blame because they could not know how ill his mind is,” Kucinski said. “You just look at the guy, and he doesn’t look as sick as he is.”

Trial testimony showed that in the months leading up to the killings, Schaffhausen told several people he had thoughts of killing his girls. His ex-wife testified that in March 2012, he called her from Minot, N.D., where he was working, and told her he “wanted to drive down there and tie me up and make me pick which child he killed and make me watch while he killed them.”

He also called Jessica repeatedly, sometimes up to 30 times a day, and threatened to kill the man she was dating.

One of his co-workers, Jeremy Michels, wrote in an email to police after the killings that Schaffhausen had said things like: “I want to go kill my kids, then my ex-wife. After her, I will go to the man’s house she is sleeping with, kill him, cut his head off, put it on a stake in my front yard and then I will sit back and have a beer.”

Schaffhausen declined to testify.

But the defense played a recording of his interview with police after the slayings. During the first two hours of the video, he is silent. In the final hour, he cried as an investigator asked him about tucking the girls into their beds. Later, he is seen on the videotape saying, “I don’t know what I want; I don’t know what I need. I want my girls back. … I need help.”

Under Wisconsin law, to reach a verdict of insanity, only 10 of 12 jurors had to find evidence showing Schaffhausen suffered from a “mental disease or defect” that led him to lack the capacity to either know his conduct was wrong or conform to requirements of the law.