For the carrot cake: Preheat the oven to 350 degrees F. Butter and flour a standard-size loaf pan and line with parchment to overhang the edges by a few inches.
Stir together the all-purpose and whole wheat flours, baking powder, cinnamon, allspice, nutmeg and salt in a medium bowl; set aside. Combine the vegetable oil, applesauce and honey in a mixer bowl and beat on medium until smooth, about 1 minute. Add the vanilla and eggs and beat until light, about 1 minute. Add the flour mixture and beat on low just until combined. Add the carrots, pecans and coconut and beat just to incorporate. Spread the batter into the prepared pan.
Bake until a tester inserted in the center comes out clean with just a few crumbs, 55 to 65 minutes. Cool on a rack for 15 minutes, then unmold and cool completely.
For the cream cheese glaze: Beat the cream cheese and butter in a medium bowl until smooth. Beat in the confectioners' sugar until smooth. Stir in the vanilla. Stir in the milk, a tablespoon at a time, to make a thick, spreadable glaze. Spoon the glaze over the cake and spread to the edges.
You can split this recipe into 2 smaller loaf pans if desired.