Using an electric mixer, preferably a large stand model, cream the butter, gradually adding the sugars. Beat in the eggs, one at a time, beating well after each addition. Blend in the vanilla. Mix the flours, baking powder, baking soda, and salt in a separate bowl. Using a wooden spoon, stir the dry ingredients into the creamed mixture, about half at a time, until uniformly blended. Stir in the oats and raisins. Cover the dough and refrigerate for 1 to 2 hours.
Preheat the oven to 350°F. Lightly butter two large baking sheets or line them with parchment paper. Using floured hands, roll the dough into approximately 1¾-inch-diameter balls. Place them on the baking sheet, evenly spaced, leaving about 3 inches in between. Bake one sheet at a time on the center oven rack for 17 to 19 minutes. (Keep a close eye on them at the end because they can overbake quickly.) When done, the cookies will be golden brown and the centers will look slightly puffed and soft. Remove from the oven right away. Cool the cookies on the baking sheet on a rack for 2 minutes, then transfer them to a rack and continue to cool.