Your local insurance will most likely not cover you for that car in Italy though, so you'll want to

I know this topic has come up a number of times but it's usually related to car rentals. Our situation is a bit different. We are house sitting in Italy in May and they have offered use of their car if we are all assured that we are covered by some sort of car insurance.
There's no way you could buy insurance in Italy for somebody else's car. Your US insurance may cover you for liability when driving someone else's car. However, I don't know if that would cover the car for fire and theft, because that would probably not be your liability. I also don't know if the coverage would extend to overseas travel. I would ask your insurance agent, and ask if there is any additional coverage for this situation. Some travel insurance may also include coverage for driving overseas.
The people you're housesitting for should internet airline ticket specials also ask their agent what is and isn't covered when someone else is driving their car, and whether they could get additional coverage internet airline ticket specials that would close any gaps, which, of course, you would pay for.
My State Farm car insurance covers anyone I authorize to drive one of my cars. We have had friends family from Australia and England here at various times and have double checked that they would be covered under our insurance internet airline ticket specials and 100% they would.
Your local insurance will most likely not cover you for that car in Italy though, so you'll want to make sure there's is sufficient. I would probably ask them to have their insurance agent email your insurance agent to confirm all is well.