Most people assume the divorce decree is the document that matters. The marriage certificate, after all, describes a union that no longer exists. Both assumptions are wrong, and both produce stalled applications in foreign jurisdictions.
Italy's recognition of US marriage certificates runs through a system of local civil registries — the comuni — and the apostille is only the first half of the document chain. The second half is where most US filings fail.
Status of Forces Agreements determine what rights a US service member's spouse carries in a foreign country. The marriage certificate is the document that proves the relationship, and its apostille is the document that makes it valid abroad.
Americans married outside the United States face a different document chain — and the apostille they need is not a US apostille, but one issued by the country where the wedding took place.