Combine milk chocolate and bittersweet chocolate in large bowl. Stir sugar and ½ cup water in medium saucepan over medium heat until sugar dissolves. Boil without stirring until syrup is deep amber color, occasionally brushing down sides of pan with wet pastry brush and swirling pan, about 10 minutes. Carefully and slowly add whipping cream (mixture will bubble vigorously). Stir over low heat until any hard caramel bits dissolve and mixture is smooth. Pour caramel over chocolate; let stand 1 minute to allow chocolate to soften, then whisk until chocolate is melted and smooth. Chill chocolate-caramel frosting until completely cool, about 2 hours. Let stand 1 hour at room temperature before continuing.