The main goal of our research was to monitor changes in the mental health of Slovak families with children with autism spectrum disorder (ASD) compared to families with neurotypical children during three waves of the COVID-19 pandemic. We focused on the prevalence of depression, anxiety, stress and different stressors of parents. In children, we explored maladaptive behavior and the availability of interventions for children with ASD. The data were collected using an extensive questionnaire including the Depression, Anxiety, and Stress Scale-42 questionnaire (DASS-42) and two subscales of the Vineland Adaptive Behavior Scales (VABS-3). The research sample consisted of a total of 506 parents, 236 of whom have a child with ASD. Parents of children with ASD reported elevated anxiety during the first wave, while changes were found in parents of neurotypical children. During the second wave, the prevalence of anxiety, depression and stress experienced by parents in both groups increased, but significantly more in parents with ASD children. The internalizing maladaptive behavior of children with ASD also increased. During the third wave, no significant differences between the groups of parents were found in stress and anxiety, but parents of ASD children scored higher in depression. Externalized maladaptive behavior of neurotypical children increased, with minimal changes in children with ASD, which can be explained by the improved therapy availability for children with ASD, also observed in our study.