Combine the flours by sifting them into a large bowl. Add the remaining dry ingredients and stir.
Cut the shortening (such as Earth Balance to make it casein free) into the flours, the way you would when making a pie dough. You should end up with walnut-size pieces in a sandy flour.
Combine the eggs and milk in a small bowl. You can use cow's milk just fine if it's not a problem for your family. I usually use original rice milk.
Make a well in the center of the dry ingredients and pour in the liquid. Stir with a rubber spatula until everything is combined.
Stir in the cornmeal, whisking fast, until it is just combined. Do not overstir.
Pour into a greased 9 by 9 by 2-inch pan or a preheated greased cast iron skillet. Slide it into the oven. Bake for 20 to 25 minutes, or until the sides of the cornbread are slightly shrinking from the pan and a toothpick comes out clean.