Microwave chocolate with 1/4 cup milk in microwavable bowl on Medium-high for 1-2 minutes; stir chocolate halfway during cooking time. Do not overheat. Chocolate will continue to melt while being stirred.
Cream butter and shortening with electric mixer. Add vanilla.
Gradually add sugar, one cup at time, beating well on medium speed. Scrape sides and bottom of bowl often.
When all sugar has been mixed in, icing will appear dry.
Add remaining 1/4 cup milk and beat at medium speed until light and fluffy.