Preheat the oven to 350° F. Grease and flour a Bundt pan.
In a large bowl, whisk the flour, baking soda, and salt together. Add the sugar and mix well. Add the bananas, pineapple with the juice, oil, eggs, and vanilla and stir until combined.
Pour into the prepared pan and bake for 1 hour and 10 minutes to 1 hour and 20 minutes or until golden brown and a toothpick inserted in the middle comes out clean. Cool completely in the pan before removing.
For the icing:
Combine the softened cream cheese, vanilla, sugar, and 2 teaspoons of milk or heavy cream in a medium bowl. Stir until combined adding more milk or cream to get the icing to the consistency you want. It should be thick but pourable. Drizzle the icing on the cake once it has cooled and been removed from the baking pan.
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