Heat oven to 375°F In medium bowl, stir cookie mix and butter until well mixed (mixture will be crumbly).
Reserve 1 1/2 cups crumb mixture; set aside. In ungreased 9-inch glass pie plate, press remaining mixture over bottom and up side of plate; prick with fork. Bake 16 to 18 minutes or until light golden brown. Cool completely, about 1 hour.
Meanwhile, on ungreased cookie sheet, sprinkle remaining crumb mixture. Bake 10 to 11 minutes or until edges of crumb mixture begin to brown. Cool on cookie sheet, about 30 minutes.
While crust and crumb mixture are cooling, place sherbet and ice cream in refrigerator to soften. Scoop half of softened sherbet over crust; spread to cover crust. Sprinkle with 1/2 cup crumbs. Scoop all of softened ice cream over sherbet and crumbs; spread to cover. Sprinkle with 1/2 cup crumbs. Scoop remaining half of sherbet over ice cream and crumbs. Sprinkle with remaining 1/2 cup crumbs. Freeze until firm, 4 to 6 hours or overnight. Let stand 15 minutes to soften before cutting.