In a bowl, whisk together the milk, yogurt, and honey. Cover and refrigerate until ready to serve. When ready to serve, peel and seed the melons and cut into 1-inch cubes. Combine them in a bowl, toss lightly, and divide the mixture among dessert bowls (preferably glass, so that you can see the melon colors). Drizzle yogurt sauce on top of the fruit. Sprinkle each serving with about 2 teaspoons brown sugar and serve with lime wedges to squeeze over the fruit at the table.
Recipe courtesy of Gale Gand, Butter Sugar Flour Eggs by Gale Gand, Rick Tramonto, Julia Moskin: Clarkson N. Potter Publishers, 1999