I found this recipe online, and I was surprised that it had not been posted here. I usually double this recipe and freeze one loaf. I have many banana bread recipes, but Mark Bittman has deemed this one "the ultimate."
Preheat the oven to 350 degrees F. Grease a 9″x5″ loaf pan.
In a medium bowl, mix together the flours, salt, and baking powder; set aside.
With an electric mixer, cream the butter with the sugar, then slowly beat in the eggs, bananas, and vanilla.
Slowly add the dry ingredients to the wet ingredients and beat just until combined (do not mix it up too much), being sure to scrape down the edges of the bowl a few times. Gently fold in the chocolate chips (if using).
Pour the batter into the loaf pan and bake for 45 to 60 minutes (mine takes about 55 minutes), until nicely browned.
A toothpick inserted into the center of the bread will come out fairly clean when it is done, but because of the bananas this bread will remain moister than most.
Cool on a rack for 15 minutes before removing from the pan.