Wash strawberries, pat dry, hull and halve (if they are large). Remove any stems from blueberries; rinse berries and pat dry. Rinse blackberries and pat dry. (Do not rinse raspberries.) Put berries in a large bowl. Toss gently and transfer to an 8-by-4- inch (2-quart) loaf pan.
Pour 1/2 cup juice in a small bowl. Sprinkle gelatin on top and let stand and soften for 5 minutes. Meanwhile, pour 1 1/2 cups juice into a large, heat-proof bowl. Microwave for 2 minutes at full power, until hot. Microwave softened gelatin at full power for 30 seconds to dissolve it. Stir gelatin into hot juice. Stir in remaining 2 cups room-temperature juice.
Gradually pour 3 cups juice-gelatin mixture over berries. Chill uncovered for 30 minutes to set. Drizzle remaining juice into mold (cover all berries) and chill for at least 2 1/2 hours, until firm.
To unmold, place pan in hot water for 10 seconds. Remove from water; invert an oblong platter over pan and flip. Gelatin should loosen. If it doesn't, return pan to hot water. Blot any liquid with a paper towel.