In a large bowl, combine the all-purpose flour and masa harina and whisk until combined. And the oil and use a spatula to mix until completely incorporated.
Dissolve the salt in the water and pour ⅔ cup of it over the flour mixture and mix with a fork. The dough will be clumpy. Mix in the remaining water.
Scoop the dough onto a lightly floured work surface and knead until smooth. It should be a medium-stiff consistency, not soft like bread dough.
Divide the dough into 8 or 12 portions and roll each into a ball. Set them on a plate, cover with plastic wrap, and let rest for 30 minutes.
Heat a cast-iron skillet to medium heat.
Place a piece of parchment paper on each side of a tortilla press and place a dough ball in the center of the bottom circle. Close the top and press down hard to flatten. Alternatively, you can use a rolling pin to roll it out between 2 pieces of parchment paper.
Place the tortilla onto the dry hot skillet for 30 to 45 seconds. Flip and cook for 30 to 45 seconds more. Don't overcook the tortilla or it will become crisp and less pliable.
Remove and wrap in a kitchen towel to keep warm. Repeat with remaining dough. The skillet will get hotter as you work, so adjust your heat and timing, if necessary.