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Our church uses piCal, and I think it will fit your needs...
Using the categories and category permissions, you can customize what each group of users sees on their calendars. Also, when you submit a new event for the calendar, you can select multiple categories, and whether the event is public, or private (yourself, or a user group).
With a careful use of categories, you can even use it to track resources (rooms, audio/visual equipment).
If you really want separate calendars, there are instructions for installing multiple copies of piCal on your site.
