Heath and Deborah Campbell left state Superior Court in Hunterdon County on Thursday without speaking to reporters, but attorney Pasquale Giannetta said he was hopeful the children would be returned to their parents.
"I'm pretty confident," he said. "We took a step forward today. As long as it goes in the right direction, they'll have the children back."
Due to privacy rules governing family court matters, Giannetta said he was not allowed to discuss what occurred in the hearing before state Superior Court Judge Peter Buchsbaum.
But he said Buchsbaum increased the Campbells' visitation from one day per week to three. The visits last about 90 minutes, according to Giannetta.
It was not immediately clear when Buchsbaum would hear the case again.
Representatives of the Division of Youth and Family Services, who are forbidden by agency policy to discuss individual cases publicly, also did not comment outside the courthouse.
Heath Campbell has 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."
The family made headlines in December when a supermarket refused to decorate a birthday cake with their son's name.
DYFS removed Adolf and younger sisters JoyceLynn Aryan Nation Campbell and Honszlynn Hinler Jeannie Campbell from the home in January.
DYFS officials have not said why the children were removed. Heath Campbell believes the removal was prompted by the publicity surrounding their names.
"They said it's not about the newspaper articles, but they took them because of their name - I don't care what anybody says," Campbell told The Associated Press in January.
Campbell also told the AP that the state was relying on unproven accusations made by a neighbor and by an ex-wife who charged him with abusing her years ago.
