Two children watch an American Army jeep driving through the ruins of Saint-Lo, Normandy, in August 1944. Photo: Galerie Bilderwelt/Getty Images When he was 28, Burkhard Bilger learned a jarring family secret: Shortly after World War II, his grandfather spent two years in jail while on trial as an accused Nazi war criminal. The revelation shocked Mr. Bilger. His parents, who moved to the U.S. from Germany in 1962, seldom spoke about their Nazi-era upbringing. Mr. Bilger, who was born in Oklahoma a year and half after his parents’ emigration, similarly avoided calling attention to a heritage that could give...