Are ethnic Italians with black hair and brown eyes considered to be caucasian?

Yes, of course

Italians are western Europeans and are considered white (caucasian), even the swarthy ones.

Historically many Italians who came to the United States were considered "off-white" or swarthy and often discriminated for their Catholic faith as well. However, first of all, not all Italians are dark haired, dark eyes. In fact, around half of all Italian in Italy according to a survey by Cavalli-Sforza has light eyes (blue, green, hazel) and that the majority of Italians (85%) do NOT have Black hair, but rather brown, and a blonde minority (10%).