Prepare and bake cake according to package directions, using a greased and floured 13-in. x 9-in. baking pan. Cool for 10 minutes before inverting onto a wire rack. Cool completely.
For filling, in a large bowl, cream the butter, shortening and sugar until light and fluffy. In a small saucepan, heat milk to 140°; cool for 2 minutes. Gradually add to the creamed mixture. Beat until sugar is dissolved. Stir in vanilla.
Split cake into two horizontal layers; spread filling over bottom cake layer. Top with remaining cake layer.
For glaze, in a large saucepan, combine the sugar, cocoa and cornstarch. Gradually add water. Bring to a boil; cook and stir for 2 minutes or until thickened.
Remove from the heat; stir in butter and vanilla until glaze is smooth. Cool to lukewarm. Spread over top of the cake. Let stand until set. Refrigerate leftovers.