The Luftwaffe in France during WWII
America currently uses air power against its opponents in Iraq and Afghanistan. None of any Iraqi nor Afghani resistance groups has any air power of its own, nor any armored ground forces. It is not clear to me that the Nazis used air power to attack the French resistance.
Clearly, America is more unaware of the problems of such an approach than its NATO allies. Here is a NATO commander of the International Security Assistance Force, quoted in Bloomberg
These incidents were mainly exchange of small arms fire and skirmishes. ISAF used air power only against positively identified groups of insurgents that targeted one helicopter, which acted in self defense.
Word on the street is that violence in Afghanistan is reaching higher and higher levels. This post, from Vets Voice, says that it is more dangerous, on a per capita basis, for a member of the US Armed Forces to be in Afghanistan now, than in Iraq. The author goes on to say that this recent change is the first time that has happened.
Sometime this summer the war in Afghanistan will surpass the American War of Independence in duration, and become America's second longest war ever. The Iraq War will pass the American War of Independence in duration next year.