Government responses to COVID-19 included workplace and childcare closures. Many parents worked from home while caring for preschool children. Media use increased worldwide for adults and young children. This study examined how government responses were linked to family media use by testing whether policy stringency predicted preschool children's screen time and parents' motivations for child media use. Data were analyzed from 2,365 parents of 2- to 5-year-old children in five countries: Canada, the United States, Israel, Sweden, and New Zealand. Higher stringency was associated with decreased screen time, though changes in screen time depended on parental income and education. Children from lower-resourced homes had the highest screen time while experiencing low stringency levels. Parents' motivations for children's media use to calm their children and for their child's enjoyment were less likely with higher stringency. Motivations also depended on child age; parents were more likely to use media to calm their younger children than their older children. Media motivations also differed with family resources; less-resourced families were more likely to use media for calming their children. Our discussion focuses on how structural factors (policies, supports, and resources for parents) relate to family media patterns and how future research can inform our understanding of policy-related outcomes on children.