Christian, Muslim, Jew
Speaking of the Jews, Razib has an interesting post (following up on this post, from last year) attacking the intellectual seriousness of the term "Judeo-Christian." Among other things, he argues that in terms of historical beliefs and practices, it makes more sense to talk about a Judeo-Islamic tradition, with Christianity, trinities and all, as the outlier, than it does to lump the Christians and the Jews together.
Given that the term in question evolved, in part, as a characteristically American form of politeness - a way to make a Jewish minority in a largely-Christian society feel welcomed and at home - I don't think it's a surprise that it's somewhat wanting in the intellectual-rigor department. But I think there are two defenses to be made of it. The first is that it's most often employed in the context of intra-Western debates over secularism, atheism, the culture war, and so forth, rather than in the context of Islam - and in a landscape like the post-Enlightenment West, where traditional religion has often been opposed by secular ideologies of various stripes, Jews and Christians would seem to have enough in common to constitute a Judeo-Christian axis (if you will) that can be reasonably contrasted with worldviews ranging from Comtean positivism to Marxism and National Socialism. (It's not a coincidence that the term "Judeo-Christian" was initially popularized during decades when the latter two ideologies were ascendant.)
Throw Islam into the mix, obviously, and the term makes less immediate sense. Razib allows that self-consciously modernized faiths like Reform Judaism and liberal Protestantism have more in common with one another than either does with contemporary Islam, but he makes the case that "Rabbinical Judaism, the dominant form of Judaism between 500 to 1800, resembles Islam much more than Christianity," and that even the Judaizing tendencies in post-Reformation Christianity don't create a practical affinity with Judaism comparable to the similarities between how Muslims and Jews worship the God of Abraham.
His brief is plausibly argued (though he glosses rather quickly over the implications of the Maimonidean-Scholastic connection), so let me just offer one possible response: Namely, that you could arguably rest a case for a deeper Judeo-Christian than Judeo-Muslim affinity on how the junior religion relates to the parent faith. Both Christianity and Islam are essentially supersessionist, obviously, but I suspect that the Christian decision to swallow the Hebrew Bible whole into its scripture - and to preserve, rather than elide, Jesus' own obvious self-understanding as a Jew - ultimately creates deeper grounds for dialogue than does Islam's insistence that the narrative of the Hebrew scriptures was deliberately corrupted and required correction from Muhammed.
Put another way, Christian tradition seems to have more respect for the essential integrity and God-givenness of pre-Christian Judaism than does Islamic tradition. This makes it difficult to imagine a Muslim version of the sort of rethinking of what, precisely, supersessionism means than we've seen from Evangelicals and Catholics in this century - a rethinking that's been crucial for the development of Judeo-Christian dialogue. And by the same token, there's no equivalent in the foundational narrative of Islam to the striking Jewishness of Jesus, a quality which would seem to make Jewish engagement with the Gospel narratives - and Christian engagement with that engagement - more plausible and intellectually fruitful in the long run than Jewish engagement with the figure of Muhammed.
Admittedly, though, these suggestion are entirely provisional, and perhaps hopelessly timebound. The potential for fruitful Jewish-Christian dialogue was not readily apparent, to put it mildly, during many periods of Christian history; there were periods when Jewish-Islamic dialogue was in better shape that it is today; and it may be that Muslim-Jewish dialogue in, say the 24th century will look a lot like Christian-Jewish dialogue does at present, the various scriptural tumbling blocks notwithstanding. And if that dialogue is taking place between religious scholars in a peaceful Israel and Palestine, I'll be delighted to have my theory disproven.