Preheat oven to 350F. Grease and flour 3 (9-inch) round cake pans.
To prepare cake, melt chocolate in microwave; let cool. Stir together flour, baking powder and salt. Combine butter and shortening and beat until fluffy, about 1 minute. Gradually beat in sugar. Add cooled chocolate and vanilla; beat well. Add eggs, one at a time; beat until light, about 2 minutes.
Combine baking soda and vinegar in a medium bowl. Mixture will foam. Add buttermilk. Add flour mixture and buttermilk mixture alternately to chocolate mixture, beating until smooth.
Divide batter among pans. Bake 30 to 45 minutes. Let cool and frost.
To prepare frosting, beat butter until light and creamy, about 2 minutes. Add cocoa powder and vanilla; beat until well combined. Add remaining ingredients; beat until fluffy.