The novel coronavirus (COVID-19) outbreak has forced parents and children to adopt significant changes in their daily routine, which has been a big challenge for families, with important implications for family stress. In this study, we aimed to analyze the potential risk and protective factors for parents' and children's well-being during a potentially traumatic event such as the COVID-19 quarantine. Specifically, we investigated parents' and children's well-being, parental stress, and children's resilience. The study involved 463 Italian parents of children aged 5-17. All participants completed an online survey consisting of the Psychological General Well Being Index (PGWB) to assess parental well-being, the Strengths and Difficulties Questionnaire (SDQ) to measure children's well-being, the Parent Stress Scale (PSS) to investigate parental stress, and the Child and Youth Resilience Measure (CYRM-R) to measure children's resilience. The results show that confinement measures and changes in daily routine negatively affect parents' psychological dimensions, thus exposing children to a significant risk for their well-being. Our results also detect some risk factors for psychological maladjustments, such as parental stress, lower levels of resilience in children, changes in working conditions, and parental psychological, physical, or genetic problems. In this study, we attempted to identify the personal and contextual variables involved in the psychological adjustment to the COVID-19 quarantine to identify families at risk for maladjustment and pave the way for ad hoc intervention programs intended to support them. Our data show promising results for the early detection of the determinants of families' psychological health. It is important to focus attention on the needs of families and children-including their mental health-to mitigate the health and economic implications of the COVID-19 pandemic.