Background Genetically informed studies have provided mixed findings as to what extent parental substance misuse is associated with offspring substance misuse and antisocial behavior due to shared environmental and genetic factors. Methods We linked data from nationwide registries for a cohort of 2 476 198 offspring born in Sweden 1958-1995 and their parents. Substance misuse was defined as International Classification of Diseases diagnoses of alcohol/drug use disorders or alcohol/drug-related criminal convictions. Quantitative genetic offspring-of-siblings analyses in offspring of monozygotic and dizygotic twin, full-sibling, and half-sibling parents were conducted. Results Both maternal and paternal substance misuse were robustly associated with offspring substance misuse [maternal adjusted hazard ratio (aHR) = 1.83 (95% confidence interval (CI) 1.80-1.87); paternal aHR = 1.96 (1.94-1.98)] and criminal convictions [maternal aHR = 1.56 (1.54-1.58); paternal aHR = 1.66 (1.64-1.67)]. Additive genetic effects explained 42% (95% CI 25-56%) and 46% (36-55%) of the variance in maternal and paternal substance misuse, respectively, and between 36 and 44% of the variance in substance misuse and criminality in offspring. The associations between parental substance misuse and offspring outcomes were mostly due to additive genetic effects, which explained 54-85% of the parent-offspring covariance. However, both nuclear and extended family environmental factors also contributed to the associations, especially with offspring substance misuse. Conclusions Our findings from a large offspring-of-siblings study indicate that shared genetic influences mostly explain the associations between parental substance misuse and both offspring substance misuse and criminality, but we also found evidence for the contribution of environmental factors shared by members of nuclear and extended families.