I'm working in Italy for a company that provides me health insurance while in Italy (and my family was able to get into the Italian public healthcare system). However, when we go back to the US for a visit, we have no coverage. Are there plans for people in this type of situation, and are they pretty expensive?
You are presumably confused by the fact that you are a US citizen and do not think of this visit as a regular vacation but since you are an Italian resident, you would typically be eligible for a regular travel (health) insurance contract from any private Italian insurer just like Europeans who go on a trip to the US. That's what those are for.