Invisible people shouldn't be able to see since the light either passes through or around their eyes, amirite?

Depends on how you make yourself invisible.
 
"The Shadow, mysterious character who aids the forces of law and order is, in reality, Lamont Cranston.

Years ago in India, Cranston learned many strange secrets from a Yogi priest, keeper of the the Temple of the Cobras at Delhi. He taught him the power to cloud men's minds so they cannot see him."