SARS-CoV-2 infection may impair behavior and mental health; we explored the psychological impact on parents and children who experienced COVID-19 within their families. A cross-sectional web-based survey was conducted on families attending the COVID-19 Follow-up Clinic at the Department for Women’s and Children’s Health, Padua (Italy). From April 2020 to August 2021, 75 surveys were collected from 66 families (97 parents and 129 children); almost 70% of participants had COVID-19, mostly asymptomatic/mildly symptomatic, and the median time from infection to survey compilation was 164.7 days (SD 56). Most parents (>87%) reported positive relationships with family members either before, during, or after COVID-19. More than one-third of children and adolescents were unable to adapt to isolation. Among 31 pre-school children with a median age of 3 (SD 1.7), a change of one or more functions was reported for 74.2% of cases irrespective of COVID-19 status, particularly a change in circadian rhythm (25%), in relationship with parents (42.8%), and poor emotional control (36%). Among 74 children with a median age of 10.9 years (SD 2.7), 8.1% had a score indicating a disease; however, significant impairment in attention was reported for 16.7%, along with anxiety/depression and problems with conduct in 5.6% and 6.5% of cases, respectively.