A lot of BS that is plain wrong has been said here.
First of all, the $82K (or there abouts) exemption is on income a US citizen not residing in the US earned from a non US company while working outside of the US. Go on a business trip in the US and the portion of the salary you earned in the US is not exempt.
If you are a US resident (citizen or green card holder) working for a US based company overseas, you get taxed on the lot.
As for tax treaties, all that means is that the US and the other country do not double tax you on the same money. What that means in the case of Italy, you pay your Italian income taxes and then file your US income tax return. All that happens then is that you get to deduct the tax amount you paid to Italy from the tax you owe to Uncle Sam on the money you earned in Italy. If the tax rate in Italy is higher, then you don't have to pay it again to Uncle Sam.