Many studies have shown that children of alcohol abusing parents have a higher risk for mental and behavioural disorders compared to other children. Using a retrospective population-based cohort study, based on health care and social welfare registers that include children born in Finland in 1997 and their biological parents, we evaluated whether the severity of parental alcohol abuse is related to these disorders in children. We examined (1) differences in the incidence of mental and behavioural disorders over time among the children of parents with no alcohol problems, parents with less severe alcohol problems and parents with severe alcohol problems, and (2) associations between mother’s and father’s alcohol abuse and children’s risk of disorders. Children were followed up until the age of 15. A diagnosis of mental or behavioural disorders during the follow-up was received by 15.4% of the boys and 9.0% of the girls. Both less severe alcohol abuse (HR = 1.36, 95% CI 1.14–1.61) and severe alcohol abuse (HR = 1.29, 95% CI 1.11–1.49) in mothers increased the risk of these disorders in their offspring. The corresponding figures among fathers were HR = 1.19, 95% CI 0.92–1.54 and HR = 1.16, 95% CI 1.02–1.32. Our results indicate that both maternal alcohol abuse and paternal alcohol abuse, regardless of severity, are associated with an increased risk of mental and behavioural disorders in children. It is crucial for professionals working with children to pay attention to all children whose parents have any alcohol abuse problems.