1. Preheat oven to 375°F.
2. Coat 12 muffin cups with nonstick cooking spray.
3. In a large bowl combine flour, sugar, baking powder, salt and baking soda; mix well. Set aside.
4. In a medium bowl combine bananas, eggs, oil, honey, and vanilla; mix well.
5. Add to dry ingredients; stir just to combine (do not over mix).
6. Fill muffin cups two-thirds full. Spoon 1 teaspoon of the raspberry jam on top of each; gently swirl with a large skewer or a small knife to create a marbled effect.
7. Bake 15 minutes or until a wooden toothpick inserted into the center of a muffin comes out clean. Remove pan from oven, and let muffins cool in pan several minutes.
8. Transfer muffins to a wire cooling rack; let cool completely.
9. Serve with coffee or enjoy as an evening snack.