Still, Vallejo (pronounced va-LAY-oh) is no promised land.

Stubborn racial divisions remain. The typical black family has a household income that is three-fourths of the city’s median. Nearly three out of every four members of the Police Department are white, and all of the City Council members are either Filipino or white.

Academic performance is improving in schools, but achievement gaps remain: Of the 11th graders at Jesse Bethel High School, which is in the 94591 ZIP code, 42 percent of black students and 51 percent of Hispanic ones tested proficient in English this year, compared with 63 percent of white students and 77 percent of Filipino ones.

Spencer Lane, a 17-year-old white senior at a high school where whites are in the minority, said classmates had told him that he looked as if he could shoot up a school. Ms. Yee-Ross said her mother once heard a news account of a robbery and insisted that the perpetrator had to be black. And the Johnsons have battled racial tension in their family and their business.

A white customer who had been a regular at the restaurant once asked the woman taking his order to make sure that a young black employee did not cook his food, Ms. Johnson said. When she heard commotion at the front of the restaurant, she said, she confronted the customer, who told her: “How can you have people like that working here? His pants are sagging.”

The Johnsons met in Vallejo in 2003, introduced by mutual friends. He liked her toothy smile, she liked his respect, but each harbored racial stereotypes.

Mr. Johnson, 33, assumed that she would be a devoted homemaker who would cook and clean for him. Ms. Johnson, 31, said she was impressed that he did not wear baggy pants and that “he doesn’t talk ghetto.”