High-income countries are experiencing measles reemergence as the result of suboptimal vaccine uptake and marked immunity gaps among adults. In 2017, the Italian Government introduced mandatory vaccination at school entry for ten infectious diseases, including measles. However, sustainable and effective vaccination strategies targeting adults are still lacking. We use a data-driven model of household demography to estimate the potential impact on future measles epidemiology of a novel immunization strategy, to be implemented on top of the 2017 regulation, which consists of offering measles vaccine to the parents of children who get vaccinated. Model simulations suggest that the current vaccination efforts in Italy would not be sufficient to interrupt measles transmission before 2045 because of the frequency of susceptible individuals between 17 and 44 years of age. The integration of the current policy with parental vaccination has the potential to reduce susceptible adults by 17-35%, increasing the chance of measles elimination before 2045 up to 78.9-96.5%.