According to the Member Benefits list:
"Parking is complimentary if the Disney Dining Experience member enters a Walt Disney World Theme Park or Resort for a short period of time for the sole purpose of dining. The DDE member should pay parking at the toll booth, then, after dining, present a dining receipt and parking ticket at Guest Relations/Services for a refund. When dining at a Walt Disney World resort, valet parking is also complimentary. After dining, present a dining receipt at the valet stand."
A friend of mine once found out the hard way that parking isn't complimentary on major holidays when the DDE card is not in effect (Easter, Mothers' Day, 4th of July, Thanksgiving, Christmas Eve, Christmas Day, New Year's Eve and New Year's Day).