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Objective: We investigated the risk for alcohol use disorder (AUD) and drug use disorder (DUD) in the offspring of parents with major depression (MDD) or bipolar disorder (BD), including how parent and offspring sex impact familial transmission. Method: Offspring born in Sweden during 1970–1990 in intact families with parental MDD or BD (n = 1,218,920) were examined using Swedish population registries. Hazard ratios (HRs) for AUD and DUD risk among offspring were calculated using Cox models. Results: Offspring of one parent with MDD or BD had higher risks of AUD (HR = 1.34; HR = 1.50, respectively) and DUD (HR = 1.32; HR = 1.43, respectively) than offspring of unaffected parents. Maternal MDD (HR = 1.38) had a stronger effect on offspring DUD than paternal MDD (HR = 1.26), and maternal BD (HR = 1.67) more strongly influenced offspring AUD than paternal BD (HR = 1.34). Parental MDD had stronger effects on daughters than sons for AUD (HR = 1.40 vs. HR = 1.32) and DUD (HR = 1.44 vs. HR = 1.27), whereas no sex differences were found for parental BD. Among daughters, maternal MDD had stronger effects than paternal MDD for AUD (HR = 1.48 vs. 1.32) and DUD (HR = 1.56 vs. 1.33); for sons, maternal MDD had a greater impact on DUD (HR = 1.31 vs. 1.23). Maternal BD had greater effects in daughters, both compared with sons for DUD (HR = 1.92 vs. HR = 1.37) and compared with paternal BD for AUD (HR = 1.82 vs. HR = 1.30) and DUD (HR = 1.92 vs. HR = 1.31). Conclusions: Findings demonstrate familial transmission of MDD and BD in parents to AUD and DUD in offspring. Affected mothers may be particularly influential. When sex-specific transmission occurred, it was consistently strongest from mother to daughter. Public health significance statement: This study found that offspring of parents with major depression or bipolar disorder are at increased risk for developing alcohol and drug use disorders compared with offspring of unaffected parents. Risk was especially elevated when the mother was affected, with the strongest patterns seen between mothers and daughters. These findings can inform prevention and intervention efforts, such as targeted support for mothers and daughters and family-focused strategies, to help mitigate the risk of alcohol and drug use disorders.