In a larger mixing bowl (the one that you're going be using for your stand mixer) combine the applesauce and sugar. You will then add your eggs in, one at a time.
In a small bowl mashed your bananas and add the milk and vanilla.
At this point, while your mixer is on, you will begin to add the dry ingredients and the banana mixture a little bit at a time (alternating). Combine and fold in berries.
Spray muffin tin with nonstick butter flavored spray.