To research this completely, I accessed this form the following IRS link. I looked under the section entitled Source of Earned Income. It states, "The source of your earned income is the place where you perform the services for which you receive the income. Foreign earned income is income you receive for performing personal services in a foreign country".
The question is, did you earn the differential pay for services you earned in Italy for your civilian job, or was this passive income earned? It depends if you actually did work in Italy to earn this income.