Tint frosting with yellow and orange food coloring. Transfer frosting to a gallon-size re-sealable plastic bag. Snip a corner off of the bag about 1/2-inch from the bottom.
Line a 1-1/2-quart freezer-safe bowl with plastic wrap. Freeze 30 minutes. Pipe frosting lines across the prepared bowl to resemble the watermelon rind lines. Freeze 30 minutes.
Press the softened lime sherbet against the bottom and sides of the bowl, covering the frosting lines. Cover and freeze at least 1 hour or until firm.
Spread pineapple sherbet evenly over lime sherbet layer. Cover and freeze at least 1 hour or until firm.
Stir the chocolate pieces into the softened raspberry sherbet. Carefully spoon the raspberry sherbet mixture into the center of the sherbet bowl. Smooth the top. Cover with plastic wrap and freeze at least 8 hours or until firm.
Before serving, uncover bowl. Place a serving plate on the bowl and invert. Carefully remove bowl and plastic wrap. Cut the bombe into wedges and serve immediately.