In the bowl combine the yeast, honey and ½ cup of the water. Stir gently to blend. Whisk ¼ cup of the bread flour and ¼ cup of the whole wheat flour into the yeast mixture until smooth. Cover the bowl with plastic wrap and set aside until doubled in bulk and bubbly, about 45 minutes.
Return the bowl add in the remaining ¾ cup of warm water, 1¼ cups bread flour, 1¼ cups whole wheat flour, olive oil and salt. Knead until the dough is smooth and elastic. Transfer the ball of dough to a lightly oiled bowl, turning once to coat, and let rise in a warm draft-free place, about 1 hour.
Place an oven rack in the middle position and preheat to 500˚ F.
Once the dough has risen, transfer to a lightly floured work surface, punch down the dough and divide into 8 equal pieces. Form each piece into a ball. Flatten one ball at a time into a disk, then stretch out into a 6½-7 inch circle. Transfer the rounds to a baking sheet loosely cover with clean kitchen towels.
Transfer 4 pitas, 1 at a time, onto the baking surface. Bake 2 minutes, until puffed and pale golden. Gently flip the pitas over using tongs and bake 1 minute more. Transfer to a cooling rack and let cool completely.