Line a 1-1/2-quart bowl with plastic wrap. Press slightly softened lime sherbet against the bottom and sides of bowl. Freeze, uncovered, until firm.
Spread pineapple sherbet evenly over lime sherbet layer. Freeze, uncovered, until firm. (Lime and pineapple sherbet layers should be thin.)
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.