In the Maronite Catholic Church, adherents of the Greek or Russian Orthodox Church, are allowed to take communion with the congregation. It is my understanding, however, that the reverse is not true.
In our small Maronite Catholic parish, there is a GOC couple (he is a convert from the ECUSA and she is from Jordan), occasionally show up at liturgy. Abouna administers the Holy Eucharist to them and blesses their beautiful daughter, Gabriella, with the communion cup. There is a very large and active GOC congregation nearby but this couple chooses to attend our divine liuturgy because of its adherence to the Aramaic, Syriac and Arabic languages. Other ME parishioners have assured me that in Lebanon, there is much interchange of individuals baptized into Melkite, Maronite, Chaldean and GOC rites, attending services in the different churches. Perhaps we can learn from them.
"In our small Maronite Catholic parish, there is a GOC couple (he is a convert from the ECUSA and she is from Jordan), occasionally show up at liturgy. Abouna administers the Holy Eucharist to them and blesses their beautiful daughter, Gabriella, with the communion cup."
I suspect that its because she is from Jordan that the couple does this. It is distinctly possible that what we know is going on in Lebanon is going on in Jordan too. I should note however that the Greek orthodox Archdiocese has given positive instructions to the Faithful here not to do this. I note that the new Latin bishop here has removed all former referneces to this practice from the misselettes in this diocese. As I understand it, the directives from Rome require the local ordinary to confer with his Orthodox counterpart before allowing this.