Preheat oven to 325 degrees F. In a bowl sift together the flour, baking powder, baking soda and salt.
Butter two 9-by-5-inch loaf pans and line with buttered parchment paper.
In a large bowl, using an electric mixer, beat together the butter and sugar on medium speed until fluffy, about 2 minutes. Add the beaten eggs, beating well after each addition. Add the vanilla.
Reduce the speed to low, add half the flour mixture and beat until incorporated. Beat in the milk and cream until blended. Add the remaining flour mixture and beat just until the batter is smooth. Divide the batter evenly between the prepared pans.
Bake until the top of each cake is golden and a toothpick inserted into the center comes out clean, about 1 hour. Transfer the pans to a wire rack and let cool for about 20 to 25 minutes. Remove the cakes from the pans and let cool completely.