Regulation headgear

Solution 1:

Since she's looking from the upstairs bedroom window, i.e. downward, the visors (or peaks, if you will) on their military (or any other kind of uniform) caps will in fact conceal their faces.

Solution 2:

Regulation headgear, or any other clothing item with the word "regulation" in front, simply refers to that item meeting the service's regulations (i.e. rules, guidelines, standards) for uniform wear. Here is one example for the U.S. Army.

Depending on the prescribed "uniform of the day," regulation headgear might be a helmet, a ball cap with the unit name on it, a combination cap (like your first image) a tilley, a knit cap, and so on. In contrast, non-regulation head gear includes jester hats, Mickey Mouse ears, Green Bay Packers Cheese Heads, and such.

So whether something obscures the face has nothing to do with it being regulation or not.