Jesus was a Muslim, because he submitted to one God and a messenger from Him. All prophets and messengers came with the same message - oneness of Allah and to guide human kind to morals of Islam. That has been the selected religion and will be the one till the end of the world. The confirmation of it comes from Quran.
Christian is someone who follows Christ. Jesus was Christ himself. How can he be Christian? He was not Jew because Allah SWT revealed a New Testament (Enjeel) upon him. He came to reform Jews because they were not following the deen of Musa AS.