On the other hand, in a situation like FFBA+Lined Coat, you might find a GM ruling that you need to poly-coat both, as the layer under the coat will be visible.
*facepalm*
It doesn't
actually make it invisible.
It scans the area around the wearer and adjusts its coloration to blend in.
Not only is this clearly stated in the rules (SR4A 321, AR 50), if it made the long coat "see through" such that you needed to add it to the FFBA, what then? You appear to be buckass naked?
A cloak of invisibility is pretty damn useful. An invisible cloak, on the other hand, not so much.
-Jn-
Ifriti Sophist