I always hear the term to mean something along the lines of "the Western tradition". When people say America was founded on the Judeo-Christian tradition, they really mean it came out of the tradition of thought stemming from the Old Testament, carried forward in the new, fleshed out in Christendom, and ultimately culminating in the Enlightenment.

That account, of course, ignores the influence of ancient Greek thought passed to Europe via Medieval Islamic scholars as well as through the Romans and their successors.

Honestly I think we're better off just saying "The Western Tradition". Jewish thought is certainly included in that.