Combine the flours, yeast, sugar and salt in a large bowl. Add water slowly to the flour and form into smooth and pliable dough. Add oil and knead it into the dough.
Spray a large bowl with cooking spray and transfer the dough; cover with plastic wrap or kitchen towel and set aside at room temperature for about 1½ hrs or until the dough doubles in size.
Punch the dough down and divide into 8 equal pieces. Roll each piece into a smooth ball; cover and set aside for 20 minutes.
In the meantime, place a baking stone (or an overturned baking sheet) in the oven and preheat to 425°F.
Roll each ball into disks sprinkling flour as needed. Stack the rolled disks and keep them covered to avoid drying out.
Carefully place the disks on the hot baking stone (I was able to fit 2 pitas at a time on my round baking sheet) and bake for 3-4 minutes or until they puff up and look opaque.
Remove and stack them covered in a clean kitchen towel. Enjoy with your favorite fillings and dips.