Kevin Reilly, the president for entertainment at Fox Broadcasting, said he had initially been concerned about a show that would focus on a black family and be run by three white men. But after seeing the pitch for “The Cleveland Show,” Mr. Reilly said, he was convinced it could bridge the gap between family entertainment and inappropriate humor, and fit snugly on a programming schedule between “The Simpsons” and “Family Guy.”

“They’ve figured out how to really straddle the fence on that and create a show that, tonally, comes from the character himself,” Mr. Reilly said. He added: “I’ve got 10-year-old twin boys. I do not let them watch ‘Family Guy.’ I will let them watch ‘Cleveland.’ ”

Mr. MacFarlane’s clout at Fox probably would have made it tricky for Mr. Reilly to say no: with the addition of “The Cleveland Show,” Mr. MacFarlane now produces three-quarters of the network’s Sunday-night programming (including “Family Guy” and “American Dad”), and “Family Guy” is a lucrative revenue source for the Fox television studio, generating $2 million an episode in syndication fees and more than $200 million a year in licensing and merchandise.

If that success has encouraged the audacious sensibility of his animated programs, he and his colleagues are still trying to determine how much of it belongs in “The Cleveland Show”: in a scene from the pilot episode, as Cleveland and his son prepare to depart for Virginia, they are fondly told, “Goodbye, chocolate people,” by some of the “Family Guy” characters. But the show has also amended its opening theme to remove a lyric in which Cleveland refers to his “happy black-guy face.”

Nonetheless some critics who have seen the pilot are accusing the show of racial insensitivity. In a panel discussion published in Broadcasting & Cable magazine, David Bianculli of NPR likened “The Cleveland Show” to “Amos ’n’ Andy,” and Robert Bianco of USA Today warned that Fox could face a backlash.

Darnell Hunt, the director of the Ralph J. Bunche Center for African American Studies at the University of California, Los Angeles, said that “The Cleveland Show” represented an “interesting departure” at a time when minorities remain “shamefully absent” from the casts and writing staffs of prime-time television series.