Preheat oven to 400 degrees F (200 degrees C). Grease and flour jelly roll pan or line with parchment paper.
In a large bowl, mix together flour, baking soda and white sugar. Set aside.
In a saucepan, heat 1/2 cup butter, shortening, coffee, and 1/4 cup cocoa until boiling. Stir frequently. Pour chocolate mixture over flour and sugar. Stir in buttermilk, eggs, baking soda and 1 teaspoon vanilla. Spread into jelly roll pan.
Bake for 20 minutes in the preheated oven, or until toothpick inserted in center of cake comes out clean.
While cake bakes, prepare frosting. Combine 1/2 cup butter or margarine, milk and 2 tablespoons cocoa in a saucepan. Heat to boiling, stirring constantly. Beat in confectioners' sugar and vanilla until smooth. Spread warm frosting over cake as soon as it is taken from the oven. Cool.