Combine lime juice, vodka, jalapeño pepper, sugar, salt and oil. Mix until well blended. Refrigerate.
About 1/2 hour before serving, cut cantaloupe in half, scoop out seeds. Cut melon into thin wedges and remove rind. Slice honeydew into 3-inch pieces, remove rind.
Arrange melon pieces on deep platter and spoon the dressing over them. Refrigerate 15 minutes. Serve with lime slices or wedges.