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Preheat oven to 375°F. In a mixing bowl, beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking soda and salt; beat until combined. Beat in egg, milk and vanilla. Beat in as much of the flour as you can with the mixer. Stir in remaining flour.
Divide dough in half. Knead the melted chocolate and nuts into half of the dough. Knead the miniature chocolate pieces and rum flavoring into the other half of dough. Divide each portion of dough in half.
To shape dough, line the bottom and sides of a 9-by-5-inch loaf pan with waxed paper or clear plastic wrap. Press half of the chocolate dough evenly in the pan. Top with half of the vanilla dough, the remaining chocolate dough and the remaining vanilla dough, pressing each layer firmly and evenly over the preceding layer.
Invert pan to remove dough. Peel off waxed paper or plastic wrap. Cut dough crosswise into thirds. Slice each third crosswise into 1/4-inch-thick slices. Place cookies 2 inches apart on an ungreased cookie sheet.
Bake cookies for about 10 minutes or until edges are firm and bottoms are lightly browned. Transfer cookies to wire racks; cool.