Preheat oven to 375 degrees F (190 degrees C). Grease and flour muffin cups, or use paper liners. Sift together the flour, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, cream together the shortening and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla and buttermilk. Beat in the flour mixture, mixing just until incorporated. Fold in the mashed bananas and shredded apples. Fill each muffin cup half full.
Bake in the preheated oven for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool.