Sprinkle shrimp and green onions in a lightly greased 9-inch pieplate.
Combine Swiss and Parmesan cheeses; sprinkle half of cheese mixture evenly over shrimp mixture.
Whisk together baking mix and next 3 ingredients until blended. Pour evenly over cheeses in pieplate; top with artichoke heart halves, cut sides down, and remaining cheese mixture.
Bake at 400° for 30 to 35 minutes or until a knife inserted in center comes out clean. Let stand 10 minutes before serving.