In a large bowl dissolve gelatin in boiling water. Stir in cold water and rum. Cover and chill until partially set (consistency of unbeaten egg whites), about 1 to 1-1/2 hours.
Place 1-1/2 cups of the gelatin mixture in a medium bowl; cover and set aside at room temperature. Whisk 1/2 of the dessert topping (1/4 of an 8-ounce container) into the remaining gelatin mixture until combined. Pour into a 2-quart square baking dish. Cover and chill until almost firm, about 2 hours.
Stir raspberries into reserved gelatin mixture. Spoon over top of gelatin mixture in dish. Cover and chill at least 3 hours or overnight until firm. Cut into squares to serve. Top each square with some of the remaining whipped topping. Makes 9 servings.