In a large bowl, cream the butter, shortening, peanut butter and sugars until light and fluffy, about 4 minutes. Beat in eggs and vanilla.
Combine the flour, baking soda and salt; add to creamed mixture and mix well.
Shape into 1-in. balls and place 2 in. apart on ungreased baking sheets. Flatten to 3/8-in. thickness with fork. Bake at 375° for 7-8 minutes or until golden.
Remove to wire racks to cool.
For filling, in a large bowl, beat the peanut butter, confectioners' sugar, vanilla and enough milk to achieve spreading consistency. Spread on half of the cookies and top each with another cookie.
Notes
Yields about 3 dozen cookies, so 18 cookie sandwiches.