This study aimed to understand differences in leisure, educational/work and social screen time behaviours experienced by parents and children due to COVID-19 lockdown restrictions, which may inform behaviour change strategies and policy in the transition to a COVID-normal life. Participants in the “Our Life at Home” study (n = 218 parents from Australia, 43.4 ± 6.8 years, 88% female) completed a cross-sectional online survey in April/May 2020. Parents recalled their own and their child (8.7 ± 2.0 years, 42% female) or adolescents (15.0 ± 1.5 years, 50% female) participation in nine screen time behaviours in the past month (during lockdown) and retrospectively for February 2020 (pre-lockdown), providing data on 436 individuals. Screen time behaviours included leisure (computer/laptop and tablet/smartphone for leisure, TV/videos/DVDs and game consoles); education/work (computer/laptop and tablet/smartphone for work/education); and social screen time (computer/tablet/smartphone for social communication with friends, family and work (parents only)). Wilcoxon signed-rank tests and effect sizes (r) compared the time spent in each behaviour pre-lockdown and during lockdown. Large differences were observed in social (parents: r = 0.41–0.57; children: r = 0.55–0.65; adolescents: r = 0.28–0.43) and education (children: r = 0.50–0.65 and adolescents: r = 0.25–0.37) behaviours. There were small or no differences in leisure time screen use. COVID-19 lockdown restrictions have impacted parent’s and children’s screen time, and future research and policy should consider strategies to support families to manage screen time.