Background Children and adolescents from deprived backgrounds have high rates of psychiatric problems. Parental and social factors are crucial for children's healthy and positive development, but whether psychiatric morbidity is associated with parental social marginalisation is unknown. We aimed to analyse the association between mother's and father's history of homelessness and the offspring's risk of psychiatric disorders, including substance use disorder, during childhood and adolescence. Methods We did a nationwide, register-based cohort study of 1 072 882 children and adolescents aged 0–16 years, who were living or born in Denmark between Jan 1, 1999, and Dec 31, 2015. Parental homelessness was the primary exposure, data on which were obtained from the Danish Homeless Register. The Danish Civil Registration System was used to extract the population and link offspring to parental information, and the outcome, psychiatric disorders in the offspring, was obtained from the Danish Psychiatric Central Research Register and the Danish National Patient Register. We analysed the association between parental history of homelessness and risk of psychiatric disorders in offspring by survival analysis using Poisson regression and incidence rate ratios (IRRs), adjusted for year and offspring characteristics, and additionally adjusted for parental factors (age at offspring's birth and parental psychiatric disorders). Findings 17 238 (2%) offspring had either one or two parents with a history of homelessness, and 56 330 (5%) children and adolescents were diagnosed with any psychiatric disorder during the study period. The incidence of any psychiatric disorder was 15·1 cases per 1000 person-years (95% CI 14·4–15·8) in offspring with at least one parent with a history of homelessness, compared with 6·0 per 1000 person-years (95% CI 6·0–6·1) in those whose parents had no such history (IRR 2·5 [95% CI 2·3–2·7] for mother homeless, 2·3 [2·2–2·5] for father homeless, and 2·8 [2·4–3·2] for both parents homeless, after adjustment for year and offspring characteristics). This risk remained elevated after additional adjustment for factors including parental psychiatric disorders. IRRs in offspring were increased for most specific psychiatric disorders, with the highest risk for attachment disorder when both parents had a history of homelessness (IRR 32·5 [95% CI 24·6–42·9]) and substance use disorder when only the mother had a history of homelessness (6·9 [4·9–9·7]). In offspring whose mothers had a history of both homelessness and a psychiatric disorder, 35·9% (95% CI 27·1–44·8) had been diagnosed with a psychiatric disorder by the age of 15 years. Interpretation Parental homelessness was associated with an increased risk of psychiatric disorders in offspring during childhood and adolescence. These findings have important implications for public health and policy because they suggest a need for improvement in the support of socially marginalised families to help prevent psychiatric illness in offspring. Funding University of Copenhagen, The Lundbeck Foundation Initiative for Integrated Psychiatric Research (iPSYCH).