In large bowl, beat shortening and butter with electric mixer until light and fluffy. Add vanilla; mix well. Combine sugar and cornstarch. Gradually add sugar mixture, one cup at a time, beating well on medium speed. Scrape sides and bottom of bowl often. When all sugar mixture has been mixed in, icing will appear dry.
In small bowl, combine milk and whipped topping mix powder; stir well. Add to icing mixture; beat at medium speed until light and fluffy.
Keep icing covered with damp cloth until ready to use. For best results, keep icing bowl in refrigerator when not in use. Refrigerated in an airtight container, this icing can be stored 2 weeks. Re-whip before using.