An Eastern Orthodox friend sometimes attends Mass with me and receives Communion. Is this allowed?

The U.S. Bishops Conference’s Guidelines for the Reception of Communion states:

Members of the Orthodox churches, the Assyrian Church of the East, and the Polish National Catholic Church are urged to respect the discipline of their own churches. According to Roman Catholic discipline, the Code of Canon Law does not object to the reception of Communion by Christians of these churches. (canon 844 § 3)

Basically, this means that the Catholic Church does not object to reception of Catholic Communion by Eastern Orthodox Christians but urges those Christians to respect their own church’s sacramental discipline. To the best of my knowledge, Orthodox churches as a rule strongly object to their members receiving Communion in a Catholic church. A statement of this stance can be found on the Web site of the Orthodox Church in America (www.oca.org).

In short, if your friend considers himself an Eastern Orthodox Christian, ordinarily he should respect the sacramental discipline of his own church. If he wishes to receive Communion in a Catholic church, perhaps he should seriously consider entering the Catholic Church, possibly through one of its Eastern Catholic churches.