Preheat oven to 425-degrees.
Juice 1 lemon and 1 lime. Reserve. Slice 1 lemon and 1 lime into very thin slices.
Place a few lemon and lime slices in the center of each parchment square. Place a fish filet on top. (The citrus will help to keep the fish from burning on the bottom.)
In a bowl, whisk together olive oil, salt, pepper and 1 teaspoon each lemon and lime, juices and drizzle over fish. Top each piece of fish with a few very thin slices of lemon or lime. Tightly fold the parchment paper into packages and make sure they are sealed well. Put packages on a baking sheet and bake for 8-10 minutes, depending on the size and thickness of the fish.
While the fish is cooking, put remaining citrus juices in a saucepan and bring to a boil over medium heat. Reduce by ½, stirring frequently. Remove from heat and add 1 teaspoon of sherry vinegar, 1 teaspoon of salt and honey.
Mix the lemon zest, parsley, garlic together with a slight pinch of salt and pepper for the garnish. Take care when opening as steam will escape as you open the package
Spoon the reduction over the fish and top with the garnish.
Recipe courtesy Martie Duncan of MartieKnowsParties.com.