I recently encountered a recipe for chocolate chip cookies that mixes both cake and bread flour. Why would a baker want to do this? Cake flour, after all, is typically used for its low gluten content, and bread flour is often used for its high gluten content. Mixing the two would seem to defeat the purpose of using either.
The author of this recipe probably happens to keep in his pantry (or more professionally speaking, dry store) just those two types of flour, and so has specified a mix to get a mid-level flour with moderate protein levels, tailored to his preferences. Given that the author is Jacques Torres, this is almost certainly a scaled down translation of a professional recipe, where that is not an uncommon practice (the very odd measurements support the idea of scaling and rounding; the weird flour measurements are probably the closest volume equivalent to a weight based scaled recipe).
Two commercial varieties (all purpose, and the less common pastry flour) also have protein levels in between cake flour and bread flour, with pastry flour being somewhere between cake flour and all purpose, typically.
If you happen to have all purpose (and you almost certainly do) I would suggest using it in the recipe for the total of both specialty flours. Very few cookie recipes are so fussy that it will actually matter very much.
In cookies, usually bread flour is used to make a cookie spread more and cake flour is used to make a taller cookie. Since this is a scaled down version of a professional recipe, he most likely combined them to get exactly the profile he was looking for. I agree with the other comment that at home, you can almost certainly use all purpose flour instead of blending the other two. Your cookies may not look exactly the same, but unless you happen to keep a large inventory of flours, it's probably worth it to cut that corner.