This seems like as good an excuse as any to post this.
Hmmm. Well, we are told making a veil you can see through easily from the inside is harder...
My guess is it works this way. The veil normally bends light around you, then puts it back on the path it would have followed after passing through the empty space if you had not been there. But to allow you to see, it doesn't bend light that is directed toward your eyes.
This would cause your eyes to be visible, though, so the next step is to use a second (EDIT: one-way) layer of veiling in front of your face to absorb outward-directed light reflected from your eyes (the light you actually use to see is absorbed, not reflected).
The photons that hit your eyes still don't pass through the "empty space" where you are standing (either absorbed by your eyes or by the eye-covering second layer of veiling), but this should appear only as two eye-sized spots of shadow on the surface behind you -- not very noticeable.
Unless I am missing something...
EDIT: removed redundant sentence fragment on light passing through