Preheat a grill to medium high. Lay out four 12-by-18-inch sheets of heavy-duty foil on a work surface. Combine the tomatoes, beans, olive oil, wine, garlic, red pepper flakes, oregano, 3/4 teaspoon salt and a few grinds of pepper in a large bowl. Stir well.
Drizzle the foil with olive oil. Evenly mound the kale in the center of each sheet. Season the halibut with salt and pepper and place on top of the kale. Add the mussels to the sheets, then spoon the tomato mixture on top. Bring the two short ends of the foil together and fold twice; fold in the sides to seal.
Grill the foil packets until the fish is cooked through and the mussels open, about 10 minutes. Carefully remove to a baking sheet. Grill the bread until lightly charred, 1 to 2 minutes per side. Drizzle the cut sides with olive oil and season with salt. Carefully open the foil packets; discard any unopened mussels. Sprinkle with the parsley and serve with the bread.
Put fish fillets on top of other ingredients when building a foil packet: The fish will cook through more gently without charring.