"Josephus and the New Testament" by Steve Mason has some information about the wives of Josephus garnered from various passages in the writings of Josephus. While a prisoner of the Romans during the Jewish Revolt, Josephus married a captive woman. This was his second marriage. Details of his first marriage are apparently not given.
When Josephus went with Vespasian to Alexandria in Egypt, he left the second wife behind and married a third, later claiming that as a priest it had been improper for him to marry an "impure" captive woman. This third wife gave him three sons, two of which died. He divorced this wife for "displeasing behavior". In Rome, Josephus married a fourth wife and had two additional sons by her.
It seems Josephus had reason to suppress his Herodian family ties in his writings after the fall of Jerusalem, which was effectively the end of main Herodian rule in Palestine/Israel. In the mind of Josephus, Hasmonean kingship had been superior to Herodian, primarily because it was earlier/more ancient. What's more, the leaders of the Jewish Revolt had been Herodians, including Josephus himself, therefore it was probably wise (in Rome) to emphasize the Hasmonean component of his ancestry.
The names of the three surviving sons cover the poltical gamut, Hyrcanus (Hasmonean), Justus (Hebrew?), and Agrippa (Roman/Herodian). Incidently, two of the sons of Aristobulus III were also named Agrippa and Justus.
© Charles N. Pope, US Library of Congress. All rights reserved.