Line a 1-1/2-quart bowl with plastic wrap. Press a thin layer of lime sherbet around the inside of bowl. Freeze, uncovered, until firm. Spread a thin layer of pineapple sherbet evenly over lime sherbet layer. Freeze, uncovered, until firm. Pack raspberry sherbet in center of sherbet-lined bowl. Smooth the top to resemble a cut watermelon.
Cover and freeze until firm, about 8 hours. Just before serving, uncover bowl of molded sherbet. Place a serving plate on the bowl and invert. Remove bowl and peel off plastic wrap.
Cut the bombe into wedges; press a few chocolate chips into the raspberry section of each wedge to resemble watermelon seeds.