This is really a MobileMe issue. Apparently MobileMe syncs CalDav and subscription calendars between multiple computers, but it won't display them in the web interface. See:
Apple - Support - Discussions - Subscribed Calendars? ...
If you are using MobileMe to push content to your iPhone it will push from the web interface, so you won't get any CalDav or subscription content.
However, apparently (I haven't tried this) you can have multiple "push" email accounts (say MobileMe and Zimbra) and allow both to push data to the calendar on the iPhone. You can't combine push and iTunes sync, but you could push from MobileMe and a Zimbra server (but again, that's only what I've read).
Good luck.