The RC church offers communion to Catholics. If you are not a Catholic, you aren't supposed to go up. However, if you do, very likely no one would know that you aren't Catholic and would give you communion there anyway. (When people are formally received as Catholics, there is usually a baptism-type ceremony and "First Communion" for them.)
But, you are not attending a Catholic church, and it sounds like yours is an "Open Table" arrangement. At our church, for example, the minister usually says that anyone, whether belonging to our denomination or not, is invited to participate if that person has repented and trusted Christ. (He then adds that even if someone's been a member all his life here, s/he should not eat it if those requirements are not met.)
Actually, our minister also enjoys changing how communion is served: sometimes we go up and dip bread into wine, and sometimes it gets passed around. When we go up, we eat it right there; when we are served in our chairs, we wait until everyone has been served and the minister leads us to partake together.
Elsewhere, I've never seen communion like that!... But I guess it must be very helpful for folks who bring communion to shut-ins.