Preheat oven to 325°. Grease and flour a 10-in. fluted tube pan.
In a large bowl, cream butter, peanut butter and sugars until light and fluffy. Add eggs, one at a time, beating well after each addition. Beat in vanilla. In another bowl, whisk flour, salt, baking powder and baking soda; add to creamed mixture alternately with milk, beating after each addition just until combined. Transfer to prepared pan.
Bake until a toothpick inserted in center comes out clean, 65-75 minutes. Cool in pan 5 minutes before removing to a wire rack to cool completely.
For frosting, in a large bowl, beat butter, peanut butter, sugar and salt. Beat in enough milk to achieve desired consistency. Spread over top of cake.