Research during the COVID-19 pandemic has shown a strong relationship between child symptoms, parental stress, and mental health challenges. The pandemic has changed family routines, worsening child symptomatology and parental burden. The aim of this study was to investigate how the magnitude of the perceived changes in child externalizing behavior, parental stress, and discontinuity of therapy—from before to during the COVID-19 pandemic—affected parental mental health during the pandemic. Moreover, we sought to compare these aspects cross-culturally between European countries and the USA. To these purposes, we asked Italian, Spanish, and U.S. parents of children with neurodevelopmental disabilities (NDD) to complete an online survey. Quantitative results showed that increased parental stress may have contributed to a worsening in parental psychological distress, regardless of culture. Moreover, they suggested an indirect effect of child externalizing behaviors on parents’ psychological distress via parental stress. Qualitative analyses highlighted that the lack, or discontinuity, of therapeutic activities may have been one of the key contributors to parenting burden during the COVID-19 pandemic. Finally, qualitative results highlighted resilience factors that could have decreased the risk of psychological problems during the pandemic, such as a strong sense of parental efficacy and the ability to adapt to changing family dynamics.