Whisk together the olive oil, lemon juice and zest, parsley, garlic, salt, pepper, and thyme in a large mixing bowl.
Pour mixture over fish in a large baking dish and chill for 30 minutes, covered. Alternately thread skewers with 3 pieces halibut and 3 pieces salmon.
Combine the parsley, butter, and garlic in a small bowl. Chill until stiff, then roll into a log.
Preheat the grill to medium-high heat and season the skewers with salt and pepper to taste.
4 minutes each side on the grill. Dot with butter and serve.