wagglebee, the section of the missalette which denotes those who can partake in Holy Communion says something like "those belonging to the Assyrian Church of the East, Orthodox Churches, and Polish National Churches are urged to respect their own diciplines, however the magesterium does not object to members of these churches receiving Holy Communion". I think, but I'm not sure, that the Assyrian Church of the East and the Orthodox Churches don't allow their members to receive Communion in Latin Rite churches and I don't know about the Polish National Church. To my knowledge, the Orthodox Churches do not allow Latin Rite Catholics to receive Communion in their Church. I'm not sure what they, the Orthodox, think about Eastern Rite Catholics. I hope somebody corrects me if I got anything wrong!
Thanks, I know that there is something in the Catechism about it, but I never paid much attention to it.