Lightly spoon flours into measuring cups; level with a knife. Combine flours and water in a large bowl. Press mixture together using a rubber spatula or your hands. (Mixture is dry but will stay together.) Turn the dough out onto a lightly floured surface. Knead for 3 minutes. Cover and let rest 15 minutes. Divide dough into 12 equal portions, shaping each into a ball. Roll 1 ball into a 5-inch circle (circles will be very thin) on a lightly floured surface (cover the remaining dough while working to prevent it from drying).
Heat a large nonstick skillet over medium-high heat until very hot. Place 1 dough round in pan, and cook 30 seconds or until brown spots appear, turning after about 15 seconds. Place the bread on a cooling rack over the eye of a gas burner. Hold bread over flame with tongs, turning until both sides of bread are puffed and brown spots appear. (Some chapatis will puff more than others.) Repeat procedure with remaining dough.
Note: You can use chapati flour in place of all-purpose flour and whole wheat flours, but we liked the bread made with regular flour best. You can also make this dish on an electric stovetop, although the bread will take longer to puff.