In a large bowl, combine white and purple rice, cover with water by 2 inches, and mix until water turns milky. Pour water out of bowl, add fresh water, mix and drain again. Repeat once more and drain rice in a colander. Transfer drained rice to a medium pot, add 2 cups water and the coconut milk and bring to a boil over high heat. Reduce heat to low, cover, and simmer for 25 to 30 minutes, or until liquid is absorbed. Remove from heat, uncover, and set aside.
Cut banana leaves into twelve 10- by 12-in. rectangles. Use a double layer of leaves to make six total packages. Place 1 cup of cooked rice in the center of each rectangle. Wrap up into square bundles and tie with kitchen twine or banana leaf fiber.
Heat a grill to medium-high (about 450°) or a heat cast-iron pan over medium-high heat. Place packets on grill or pan and cook for 15 minutes, or until banana leaf is charred and rice is heated through.