Parental drinking can cause harm to the offspring. A parent's diagnosis of alcohol-related liver disease (ALD) might be an opportunity to reach offspring with preventive interventions. We investigated offspring risk of adverse health outcomes throughout life, their association with their parent's educational level and diagnosis of ALD. We used nationwide health registries to identify offspring of parents diagnosed with ALD in Denmark 1996 to 2018 and age- and sex-matched comparators (20:1). We estimated the incidence rate ratios (IRRs) of hospital contacts with adverse health outcomes, overall and in socioeconomic strata. We used a self-controlled design to examine whether health outcomes were more likely to occur during the first year after the parent's ALD diagnosis. The 60,804 offspring of parents with ALD had a higher incidence rate of hospital contacts from age 15 to 60 years for psychiatric disease, poisoning, fracture or injury, alcohol-specific diagnoses, other substance abuse, and of death than comparators. Associations were stronger for offspring with low compared to high socioeconomic position: The IRR for admission due to poisoning was 2.2 versus 1.0 for offspring of an ALD parent with a primary level versus a highly educated ALD parent. Offspring had an increased risk for admission with psychiatric disease and poisoning in the year after their parent's ALD diagnosis. For example, among offspring whose first hospital contact with psychiatric disease was at age 13 to 25 years, the IRR in the first year after their parent's ALD diagnosis versus at another time was 1.29 (95% CI 1.13, 1.47). Main limitation was inability to include adverse health outcomes not involving hospital contact. Offspring of parents with ALD had a long-lasting higher rate of health outcomes associated with poor mental health and self-harm that increased shortly after their parent's diagnosis of ALD. Offspring of parents of low educational level were particularly vulnerable. This study highlights an opportunity to reach out to offspring in connection with their parent's hospitalization with ALD.