Your old visa may be valid under the law, but the policy of the US government is somewhat unclear. The passport is certainly not valid, because you're no longer a citizen of the Philippines. You might make it through US passport controls with the Philippine passport if the Philippine authorities have not listed it in the Interpol database, but I wouldn't risk it.
A valid US visa in an invalid passport may be used with a different valid passport, but the US government says that the two passports should be issued by the same country:
My old passport has already expired. My visa to travel to the United States is still valid but in my expired passport. Do I need to apply for a new visa with my new passport?
No. If your visa is still valid you can travel to the United States with your two passports, as long as the visa is valid, not damaged, and is the appropriate type of visa required for your principal purpose of travel. (Example: tourist visa, when your principal purpose of travel is tourism). Both passports (the valid and the expired one with the visa) should be from the same country. When you arrive at the U.S. port-of-entry (POE, generally an airport or land border) the Customs and Border Protection Immigration Officer will check your visa in the old passport and if s/he decides to admit you into the United States they will stamp your new passport with an admission stamp along with the annotation "VIOPP" (visa in other passport). Do not try to remove the visa from your old passport and stick it into the new valid passport. If you do so, your visa will no longer be valid.
The text above says only "should," not "must." There does not appear to be any basis for this requirement in US statutes or regulations, but the US has long asserted the requirement nonetheless. In fact, just a couple of years ago, they were asserting that the passports should also be of the same type, so they seem to be softening their position.
For more information about the former requirement, see
If you want to test this, go ahead. I suspect that a good lawyer would convince a judge to find that the requirement has no basis in law. But to do it, you'll have to do one of the following:
- get ESTA for your Italian passport, but then when you arrive ask to be admitted on the basis of your visa
- fly to Canada or Mexico and attempt to enter through the land border
- fly to the US using your Philippine passport even though you are no longer a citizen of the Philippines
That's because TIMATIC, the database that the airline would use to decide whether to let you board, reflects the "same country" requirement rather more strongly than does the US Department of State:
A passenger may enter the USA with a valid visa in an expired passport, if also holding a valid passport of the same nationality.
If you do decide to test this, you might be admitted by the immigration officer, fairly routinely, but you run a higher risk of being detained before you're admitted. You might also be refused admission. If this happens, you'll probably be pressured to withdraw your application for admission, which would let the officers send you back home, but you would avoid many of the negative consequences of being deported. If you do not withdraw your application for admission, you'll be detained until you can be brought before an immigration judge, which could be a long time as they are very overworked these days. If the immigration judge finds in your favor, you'll be released into the US. Otherwise, you'll be removed from the US, with more significant negative consequences than you would have faced had you withdrawn your application for admission.