"Postcards From Buster" is a spinoff of "Arthur" that combines live action and animation and went on the air a year ago. In the series, aimed at young elementary schoolchildren, Buster travels to 24 different states with his father and sends video postcards home.

Buster appears briefly onscreen, but mainly narrates these live-action segments, which show real children and how they live. One episode featured a family with five children, living in a trailer in Virginia, all sharing one room. In another, Buster visits a Mormon family in Utah. He has dropped in on fundamentalist Christians and Muslims as well as American Indians and Hmong. He has shown the lives of children who have only one parent, and those who live with grandparents.

Marc Brown, creator of "Arthur" and "Postcards From Buster," said in a statement: "I am disappointed by PBS's decision not to distribute the 'Postcards From Buster' 'Sugartime!' episode to public television stations. What we are trying to do in the series is connect kids with other kids by reflecting their lives. In some episodes, as in the Vermont one, we are validating children who are seldom validated. We believe that 'Postcards From Buster' does this in a very natural way -- and, as always, from the point of view of children."

Jeanne Hopkins, a spokeswoman for the show's producer, WGBH-TV of Boston, added, "We feel it's important that we not exclude kids because of what their family structure looks like." WGBH plans to broadcast the episode in March and offer it to other PBS stations.

Like the grown-ups in most of the episodes, the lesbian mothers in the "Sugartime!" segment are mainly background. "The concern really was that there's a point where background becomes foreground," Mr. Godwin said. "No matter if the parents were intended to be background, with this specific item in this particular program they might simply be foreground because of press attention to it and parental attention to it."