On the one hand, I don't really want to criticize other people's religion. On the other hand, by all general criteria, your wife is at least as much a Christian as a Mormon or a Jehovah's Witness is, and very few non-adherent Jews would describe her as an observant Jew.

https://en.wikipedia.org/wiki/Messianic_Judaism for people who are interested in a summary.

Messianic Jewish are generally not considered Jewish by the community, as their beliefs violate basic tenets of the religion. There is a lot of evidence towards these sects being used to manipulate non-religious Jews into conversion to Christianity. They are still welcome, but considered Christians.