In a large bowl, whisk together the all-purpose flour, whole wheat flour, sugar, baking powder, baking soda, cinnamon, ginger, salt, and nutmeg.
Add the canned pumpkin, oil, eggs, and molasses. Stir just until combined — don't overmix.
Grease a cake, Bundt, or loaf pan that fits your air fryer with cooking spray. Pour in the batter, filling the pan about two-thirds full.
Set the pan in the air fryer basket and bake at 320°F (160°C) for 20–25 minutes, checking for doneness starting at 18 minutes.
The cake is done when a toothpick inserted in the center comes out clean or with a few moist crumbs. Cool completely before frosting.
Beat the cream cheese, butter, powdered sugar, and milk together until smooth and spreadable.
Spread the frosting over the cooled cake, slice, and serve.