A U.S. state appeals court determined Thursday that a New Jersey couple who gave their children Nazi-inspired names should not regain custody of them.

Heath and Deborah Campbell's three small children were removed from their home by the state in January 2009.

The family drew attention after a supermarket refused to decorate a birthday cake for their son, Adolf Hitler Campbell. He and siblings Joyce Lynn Aryan Nation Campbell and Honszlynn Himler Jeannie Campbell have been in foster care.

The appeals court ruled Thursday that sufficient evidence of abuse or neglect existed because of domestic violence in the home. The court sent the case back to family court for further reconsideration.

A gag order remains in place and the parties refused to discuss the decision.

The couple received attention last year when a supermarket in New Jersey refused to write their son's name, Adolf Hitler Campbell, on his birthday cake.

The Campbells ultimately got their cake decorated at a Wal-Mart in Pennsylvania, Deborah Campbell said. About 12 people attended the birthday party on Sunday, including several children who were of mixed race, according to Heath Campbell.

"If we're so racist, then why would I have them come into my home?" he asked.The Campbells' other two children also have unusual names: JoyceLynn Aryan Nation Campbell turns 2 in a few months and Honszlynn Hinler Jeannie Campbell will be 1 in April.

Shortly after the story became known, New Jersey removed the three siblings from their parents' home and placed in the custody of the state, where they have been until the final court hearing on Thursday.

Heath Campbell said he named his son after Adolf Hitler because he liked the name and because no one else in the world would have that name.

On Tuesday he wore a pair of black boots he said were worn by a German soldier during World War II.