While it would be very convenient if such mathematical principles applied to genetics and cultural inheritance, that just isn't the case. First, ethnic and national identity (like being Italian) are not inherited through genetic processes. These are cultural structures which are learned after birth. Second, there's not really such a thing as "Italian DNA." The borders of Italy are not drawn in reference to what sorts of genetic traits people do or do not have-- in other words, Italian people aren't so significantly different in their genotypes from other nations that this is the basis for their being Italian.
Even when we consider inheritance of traits that might be thought of as classic to Italian aesthetics or stereotypical of Italian phenotypes, there's no certainty that exactly half of either parent's contributed genes will be expressed. For example, if someone's mother is Italian-- either as an Italian national or identifying with cultural heritage-- and has stereotypical Italian features like curly hair, brown eyes, and olive skin, that doesn't necessarily mean her children will have such features. Her children will inherit half of their genes from her, but this does not mean all of her inherited genes will be expressed. Even if her children were to all have similar, stereotypical Italian features, these features do not belong only to Italian people.
With that, I'm sorry to say that genetics are far messier than we'd like them to be, and culture has much more to do with being "Italian" than does any gene. It maybe of interest to you to look into something called the Founder's Effect. Some populations can be very distinctly traced to one person or place based on reduced variability in genotypes and phenotypes. It is possible that there are some Founder's Effects which may be traced to Italian territory or migration, but I do not know of any such variations.
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