Preheat oven to 350°F. Butter 13x9x2-inch metal baking pan. Whisk flour, cornmeal, sugar, salt, baking powder, and baking soda in large bowl to blend. Stir in green onions, corn, and jalapeño. Whisk buttermilk and eggs in medium bowl to blend, then whisk in melted butter. Add buttermilk mixture to dry ingredients and stir just until blended (do not overmix). Transfer batter to prepared pan or muffin tray (batter will come only about 3/4 inch up sides of pan).
Bake cornbread until lightly browned on top and tester inserted into center comes out clean, about 25 minutes. Transfer pan to rack and cool cornbread completely in pan. (Cornbread can be prepared 1 day ahead. Cover tightly with foil and store at room temperature.)