Drusus married Aemilia Lepida, daughter of Marcus Aemilius Lepidus, his second cousin. Tacitus reports that during their marriage "she had pursued her husband with ceaseless accusations". In 36, she was charged with adultery with a slave and committed suicide, "since there was no question about her guilt" (Tacitus, Annals 6.40).
Drusus' paternal grandparents were Nero Claudius Drusus and Antonia Minor. His maternal grandparents were Marcus Vipsanius Agrippa and Julia the Elder. He was adopted by his paternal great-uncle Tiberius after Tiberius' own son, Julius Caesar Drusus, had died.
Drusus Caesar was later accused of plotting against Tiberius and was imprisoned in 30, a year after his mother Agrippina the Elder and his brother Nero Caesar were arrested. He starved to death in prison in 33, reduced to chewing the stuffing of his bed (Annals 6.23).