Objective: To examine the association between parental alcohol use disorder (AUD) with and without other mental disorders and offspring AUD. Methods: Using data from Danish nationwide registers, we identified 15 477 offspring with parental AUD and 154 392 reference individuals from the general population. Parental AUD was defined as registration for AUD treatment. Parental mental disorders were identified in medical registers and comprised psychotic, mood, anxiety, personality, drug use, and other non-alcohol-related mental disorders. AUD in offspring was identified from medical, pharmacy, treatment and cause of death registers. Hazard ratios (HRs) of AUD were estimated using Cox regression models. Results: AUD in one or both parents was associated with higher risks of AUD in offspring compared with reference individuals. Paternal AUD plus other mental disorder (HR = 2.27, 95% confidence interval (CI): 2.10–2.46) and paternal AUD alone (HR = 2.21, 95% CI: 2.07–2.36) were associated with higher offspring AUD risk. Similarly, maternal AUD plus other mental disorder (HR = 3.02, 95% CI: 2.66–3.43) and maternal AUD alone (HR = 2.57, 95% CI: 2.20–3.01) were associated with higher offspring AUD risk. Conclusions: Offspring with parental AUD are at increased risk of AUD irrespective of exposure to other parental mental disorders.