Step 1

Preheat oven to 350 degrees F. Lightly coat an 8 1/2-by-4 1/2-inch loaf pan with cooking spray.

Step 2

Whisk all-purpose flour, whole-wheat flour, baking powder, baking soda and salt in a medium bowl; set aside.

Step 3

Beat cream cheese, butter and oil on medium speed in the bowl of a standing mixer fitted with the paddle attachment until creamy, about 2 minutes. Add sugar; beat until light and fluffy, about 2 minutes. Beat in egg and vanilla. With the mixer on low speed, gradually add the flour mixture alternately with banana, beginning and ending with the flour mixture. Fold in strawberries. Spoon into the prepared pan.

Step 4

Bake until a wooden skewer inserted in the center comes out clean, 65 to 75 minutes. (Shield with foil after 45 minutes, if needed, to prevent excessive browning.) Cool in the pan on a wire rack for 15 minutes. Remove from the pan and cool completely, about 1 1/2 hours.