Heat oven to 350 °F. Grease bottom only of 13" x 19" pan. Stir brownie mix, water, oil, eggs and coffee in medium bowl until well blended. Spread in pan. Bake 28-30 minutes or until toothpick inserted 2 inches away from side of pan comes out almost clean; cool completely.
Cut brownies into 1-inch squares. Place half of the squares in bottom of 3-quart glass bowl. Make pudding mix as directed on package for pudding, using milk. Pour half of the pudding over brownies in bowl. Top with half each the toffee bits and the whipped topping. Repeat with remaining brownies, pudding, toffee bits, and whipped topping.
Cover and refrigerate at least 4 hours before serving. Cover and refrigerate any remaining trifle.