Because I have a foot in both the Western and Eastern Churches, I am often asked this question: “Can I go to an Eastern Church for mass, and if so, can I receive holy communion?” First of all, you should feel free to go to any church whatsoever—in fact, if your spouse is a member of another faith community, you should participate on occasion at his/her church.
Some Protestant churches have liturgies very similar to the Roman Catholic rite—especially Lutheran, Episcopalian, et al. These churches are Western in origin, and centuries ago, these people were part of the Roman Catholic Church. Eastern liturgies, on the other hand, may sound, look, and feel quite different. These differences, however, are superficial—the essential elements of the mass are the same. Some Eastern churches are actually Catholic, i.e. “in communion with Rome,” namely Byzantine, Melkite, Maronite, Chaldean, Syro-Malabar, some Ukrainian churches, and others. On the other hand, a Church that is called “Orthodox,” i.e. Russian/ Greek Orthodox, and most Armenian churches, is not in communion with Rome.
As for receiving holy communion, of course you can and should receive in the Catholic Churches, (Maronite, Chaldean, etc. as seen above), even if their manner of giving communion looks quite different. Go with the flow! In the Maronite tradition, the host is dipped in the Precious Blood by the priest, while in the Byzantine and Melkite traditions, the host is leavened (not unleavened) bread, (a sort of untoasted crouton), soaked in the Precious Blood, and served on a spoon.
As for the Orthodox churches, the legalities of receiving holy communion can be confusing. Official Catholic teaching says that we can receive communion in an Orthodox church because their priests are validly ordained, but the Orthodox may not be comfortable with us doing so, and do not normally allow their own people to receive in our churches.
As for the Episcopalian and Lutheran churches, however, it is the exact opposite—our official teaching does not allow us to receive at their churches, whereas they place no restrictions on us receiving in their churches, or them receiving in ours.
I want to emphasize, however, that these issues are not a matter of sin. I have been in Episcopal and Lutheran churches where they expect you to receive holy communion, and are almost offended if you do not. In such cases it is a judgment call, and I recommend that you err on the side of charity. You will not be committing sin regardless of what you do, if you follow this principle.