In a large bowl, whisk together the all-purpose flour, whole-wheat flour, and salt. Slowly pour in warm water and milk while continuously mixing the dough with your hand until a shaggy dough forms. If needed, add extra water, 1 tablespoon at a time to form dough. The dough should be sticky and still slightly lumpy at this stage. Add 2 tablespoons of oil and continue to knead by hand until fully incorporated.

Turn the dough onto a lightly floured work surface and continue to knead, flouring the surface as needed to prevent sticking, until the dough is elastic and smooth, 3 to 5 minutes. Pat the dough into a rectangle and lightly brush the surface with oil. Cover with plastic wrap or a clean kitchen towel and let it rest for 20 minutes.

Use a rolling pin to roll out the dough into a thin rectangle measuring 12 by 18 inches (it's okay if there are small tears). Lightly brush the entire surface of the dough with a thin layer of oil, then dust the top lightly with flour. This will help keep the layers separate.

Starting from the long side, roll the dough into a 18-inch long log shape. Cut the dough crosswise into 8 even rounds. Flip dough rounds so the cut side is face up, then press each piece into a small flat circle. Cover with greased plastic wrap or a clean kitchen towel and let rest for 30 minutes. On a lightly floured work surface, use a rolling pin to roll out each dough piece into a 9- to 10-inch disk, frequently rotating and flipping to maintain its shape and avoid sticking. Place side by side on a lightly floured work surface and cover with plastic wrap or a kitchen towel while cooking.

Preheat an empty 10 or 12-inch cast-iron or stainless-steel skillet over medium-high heat until very hot (a drop of water dripped onto the surface should sizzle immediately), 2 to 4 minutes. Using a pastry brush, coat the hot skillet lightly with oil. Place 1 dough round into skillet and cook until the top surface is no longer sticky and a few bubbles form, and the bottom side is spotty brown, about 1 minute. Lightly brush the top with oil, flip, and cook until the second side is spotty brown, 30 to 60 seconds. While cooking, the chapati should bubble; this indicates that steam is passing through the layers, which will result in a flaky texture. This is a great indicator that the chapati dough has been properly laminated.

Repeat with remaining dough pieces, stacking cooked chapatis on a plate and keeping them covered with a clean kitchen towel until ready to serve. Serve chapatis warm.