Use the Zimbra Web Client

heh. j/k
When you accept a meeting invite, it should add it to your calendar. I assume that you're problem, right?
When you say meeting request, you're talking about a calendar event, and the problem is that in Exchange, to view it, you had to login to OWA. In Zimbra you get an invite, and you should be able to click "ACCEPT" or "DECLINE".