The Quran makes a difference between the Faithful (later called Muslim) and the Christians and the Jews. As to the message of the Quran, the Faith (later called Islam) is neither Judaism nor Christianity, nor is it a new religion founded by Muhammad, but rather a renewal of the religion that confirms and clarifies the Word of God that has come to Noah, Abraham and the Jewish prophets, for all people.
In my view, the Message of the Quran is much closer to the teachings according to the Gospel accounts than Christian and Islamic scholarly teachings are. Christians differ from in that they believe in the Word that has come to us through Jesus (p.b.u.h) but not to Muhammad (p.b.u.h). In contrast to the schism between Judaism and Christianity which took place after Jesus (p.b.u.h) left our world, the schism between Christianity and Islam already began in the active time of Muhammad (p.b.u.h.) through the refusal of the Quran and its Messenger by the Christians.
In the following, Islamic scholars also refused the Torah and the Gospel as writings of the "disbelievers" who rejected the Quran (although those who wrote them lived long time before Muhammad (p.b.u.h), and although, in my view, the Quran incites to accept and to follow the Gospel as it was available in the time of Muhammad). Many claim that there must have been an original Gospel writing that had later been corrupted (although there is not the faintest hint that a such original writing ever existed, neither in historical sources nor in the Quran).
This comes along with the misunderstanding, both of Muslim and Christians, that the accounts according to Mark, according to Luke, according to John and the one probably falsely attributed to Matthew are the Gospel/Injil. But the Gospel is the "Good Speel"="Euangelion": the Good Message. The Gospel is the Message, not a book.
Another obstacle is that the Gospel accounts seem to contradict the Quran. Many contradictions can however be resolved or at least explained.
I am currently working on an edition comprising the four canonical Gospels, the relevant passages of the Quran, the collection of Hadith falsely attributed to Thomas, some Islamic Hadith, cross-references to Jewish, Christian and Islamic sources and comments from an informed Muslim view. I am doing this for the Muslims in order to dig a little bit of the buried path to the Word that came to us through the penultimate prophet and Messiah.