The term "Italian" is used to describe a nationality or ethnicity and is not a term that pertains to race. It is impossible, therefore, to place all Italians into one racial classification, since the population is comprised of people of various races.
In the United States, the term "white" is used to refer to people of European descent. In other nations, however, it is more common to associate with one's ethnicity. Ethnicity is not strictly a classification of race, but is rather one of culture. It is possible that people who self-identify as being of Italian ethnicity would be classified under various racial categories in the United States.
An example of how ethnicity and race are differentiated in the United States is the classification of "White (Hispanic)" and "White (non-Hispanic)." The United States government considers those of Hispanic descent white. It, however, provides the Hispanic sub-category for those who wish to self-identify as being of Hispanic ethnicity. Ethnicity is not necessarily synonymous with nationality. Ethnicity can be an association through culture, nationality, heritage or religion.
Nationality is simply an explanation of someone's country of birth. It is possible, therefore, for some Italians to self-identify their nationality as Italian, but their ethnicity as something else, and their race as something other than either their nationality or their ethnicity.