Italians are on of those groups who are associated more with their ethnicity than their race (like Jews, for instance). Not quite seen as "pure" white by other Americans, yet seen as nothing but white by the government. Their sort of in between, which makes it OK to stereotype them, enjoy what they brought to American society and give them no recognition whatsoever.
Did you know 78% of teenage Americans think all Italians have a connection to the Mafia, as do 74% of adults? Pretty soon, when people think of Italians, they'll completely forget their rich heritage, and just think about swarthy Jersey Shore jackasses, Mafia, and Pizza.