Preheat oven to 375 degrees F. In a medium bowl, combine the tomatoes, garlic, onion, basil, and parsley. In a small bowl, whisk together balsamic, olive oil, mustard, salt, and pepper.
Cut 4 18×12 inch sheets of parchment paper and arrange on the counter. Place one fish fillet in the center of each sheet. Top each fillet with 1/4 of the tomato mixture and 1/4 of the olive oil mixture. Lift the short sides of the paper and fold the edges together twice to seal them. Leave some room in the packet for heat expansion, you don’t want them too tight.
Place the fish packets on a cookie sheet and bake for 20-25 minutes or until fish flakes when you test it with a fork. Be mindful of steam when unwrapping fish packets to serve.