Preheat the oven to 350 degrees. Grease and flour a 10 inch bundt pan.
Place the chocolate chips in a heat proof bowl and melt them either over a shallow pan of simmering water or in the microwave. Set aside.
Place the bananas in another small bowl and mash with a fork. Set aside.
Place the strawberry jam in another bowl and set aside.
In the bowl of an electric mixer, beat eggs on high speed until they're light and foamy. Add the sugar in four separate additions, beating for about a minute between each one. Continue to beat until mixture is thick, about 5 minutes on high speed.
Meanwhile, in another large mixing bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the vegetable oil to the egg mixture, scraping down the sides of the bowl as needed. Continue to beat for about a minute on medium high speed. Stir in the buttermilk and vanilla.
Remove the bowl from the mixer and gently fold in the dry ingredients. Pour about 1 1/2 cups of the batter over the melted chocolate and stir until blended. Pour another 1 1/2 cups of batter over the strawberry jam and stir until blended. Fold the mashed bananas into the remaining batter.
Pour about a 1/3 of the banana batter into the bottom of the bundt pan, followed by the chocolate batter, another 1/3 of the banana batter, all of the strawberry batter, then the final 1/3 of the banana batter. Use a knife to gently swirl the batters together.
Bake the cake for 65 to 70 minutes or until a toothpick inserted in the center comes out clean. Allow the cake to cool in the pan for 15 minutes then invert it onto a cake plate. Allow to cool completely before glazing.