Let butter and eggs stand at room temperature 30 minutes. Preheat oven to 350 degrees F. Grease bottoms of two 8-inch round cake pans. Line bottoms with waxed paper or parchment paper. Grease and flour; set aside.
In large bowl beat butter on medium speed 30 seconds; gradually beat in sugar to combine. Add eggs one at a time, beating well after each addition. In bowl combine banana, sour cream, milk, and vanilla. In another bowl combine flour, baking powder, salt, and soda. Alternately beat flour mixture and banana mixture into butter mixture on low.
In small bowl combine 2/3 cup batter, the 1/2 cup strawberry jam, and food coloring. In separate bowl combine 2/3 cup batter and melted chocolate. Spread plain batter in prepared pans. Spoon flavored batters on each plain batter; gently swirl with knife.
Bake 30-35 minutes, until wooden pick inserted near centers comes out clean. Cool in pans on racks 10 minutes. Remove from pans, peel off paper, cool. Place one layer flat side down on plate. Top with jam. Stack second layer flat side down.