In a large mixing bowl, combine all-purpose flour, semolina flour, and salt.
Dissolve yeast in warm water and let it sit for 5 minutes until frothy.
Gradually add the yeast mixture to the flour mixture, kneading until a smooth and elastic dough forms.
Cover the dough with a damp cloth and let it rise in a warm place for 1 hour until doubled in size.
Preheat the oven to 475°F (245°C) with a baking stone or inverted baking sheet inside.
Divide the dough into 6 equal portions and roll each piece out on a floured surface into very thin circles, about 10 inches in diameter.
Place one flatbread onto the preheated stone or baking sheet and bake for about 60-90 seconds, until it puffs up and starts to brown.
Flip the flatbread and bake for an additional 30 seconds.
Remove from oven and immediately wrap in a clean kitchen towel to keep soft. Repeat with the remaining dough.
In a food processor, combine olives, capers, minced garlic, parsley, and lemon zest.
Pulse until coarsely chopped.
While the processor is running, slowly drizzle in olive oil until the mixture becomes a spreadable paste.
Season with salt and pepper to taste.