By the time Mohammed died, the Christians and Jews of Arabia had been totally subjugated. The history of his relations with the Jews and Christians determined how they have been treated over the past 1400 years.
In the very beginning in Mecca, Mohammed said that his prophecies came via the angel Gabriel, who was the angel who spoke to Moses. In Mecca he presented himself as a prophet in the line of Jewish prophets. However, the Koran also talks about Judgement Day, which is a Christian concept. Basically, Islam is both a Christian and Jewish heresy.
Later in Medina, Mohammed persecuted both Jews and Christians. Jihad destroyed the Arab polytheists and caused both Jews and Christians to submit to Islam.
Islam has a dual nature in dealing with the Jews and Christians. It says that Muslims, Christians and Jews are members of the Family of Abraham and yet, they are mortal enemies to be subjugated.
You cannot understand jihad with Israel without knowing the Islamic doctrine of the Christians and Jews.