Should I invite my Jewish neighbor to my church?

Yes, but it would be even better to locate a nearby messianic congregation and invite your Jewish neighbor to attend services with you. However, before you invite him to church, you will need to build some bridges and develop sensitivities toward the Jewish people.

"You Bring the Bagels, I'll Bring the Gospel: Sharing the Messiah with Your Jewish Neighbor" is an excellent book that contains detailed information on this subject.