Plus it'd also be a pretty controversial topic in a series about pagan pantheons. The only way to reconcile the two would be to treat the halfbloods as Nephilim, which are a hybrid cross between divine but fallen angels and humans. In the Bible they're actually said to have become "men of renown" and "heroes of men" or something along those lines.
Come to think of it, Shin Megami Tensei does something like that. It has a huge number of deities and beings from other religions, but they're all considered demons and stuff.

Obviously you know I'm Christian, but I still think it'd be something interesting to see.