Line a 13 by 9-inch baking pan with heavy-duty aluminum foil.
Place half of ice-cream sandwiches evenly over bottom of pan, completely covering bottom, cutting sandwiches to fit, if necessary. Top evenly with banana slices. Pour hot fudge sauce over bananas. Top with cherries and 1/2 of the toffee bits and pour butterscotch evenly on top. Layer with remaining ice cream sandwiches and spread whipped topping over sandwiches; sprinkle with remaining toffee bits.
Cover and freeze for at least 4 hours. Remove from pan, using foil handles. Cut into squares and serve.