Mesh will also be an issue, depending on it's spacing. The door of your microwave over has holes that let visible light through (you can see your food), but are still small enough to block the microwave's energy (your eyeballs don't heat up).
A Faraday cage needs to nearly surround you, I doubt a metal roof will block much, the signal comes from things often ~6 stories tall, meaning the reception is mostly horizontal, not vertical (you will block a lot of the sun's energy).
To be a cage, there needs to be electrical continuity, so rebar (most office buildings, airports, etc) forms a mesh, but doesn't normally form a 360 degree cage, and it's spacing is too wide - so your reception is generally fine, perhaps just attenuated some in a heavily reinforced building. But inside an elevator, it's generally dead (or severely attenuated) - you're in a nearly perfect Faraday cage.
Rebar, like in a bridge overpass, acts like a very large antenna, not a faraday cage. So it kills very long wavelengths - drive under a bridge, AM radio goes out, but phone calls usually don't drop. Go thru a tunnel though, and once you're sufficiently deep in it, to be nearly surrounded on all sides, and your cell won't work. In the tunnel's case, it's not really a Faraday cage doing the blocking, as it is the shear mass of metal surrounding you in every direction. A Faraday cage doesn't require massive amounts of metal, a tin foil tent would kill almost all signals.
All this said, another way to think about your roof question is to think of other incomplete Faraday cages you use every day, like your car... :-)
Find a friend with a metal roof though, nothing beats an empirical evidence.