YES — Your family is entitled to this grant, even if you die in another EU country. Your family should apply for a death grant from the health insurance institution where you are registered in your country of residence. They will forward your request to the right authority.
NO — You live in Italy and receive an Italian pension. As a result, your husband is only entitled to an Italian death grant, whether you are also receiving pensions from other countries or not. Unfortunately, death grants do not exist in Italy. As a result, your husband will not be entitled to any death grant when you pass away.