IMPORTANCE: Paternal depression during the postnatal period has been associated with adverse child outcomes. Family environment has been reported as a pathway for risk transmission from fathers to children. The influence of paternal depression during the postnatal period on offspring depression remains to be clarified. OBJECTIVE: To investigate the association between paternal depression in the postnatal period and offspring depression and explore potential mediating and moderating factors that influence any association between paternal and offspring depression. DESIGN, SETTING, AND PARTICIPANTS: This prospective study of a UK community-based birth cohort (the Avon Longitudinal Study of Parents and Children) of parents and their adolescent offspring investigated associations between paternal depression during the postnatal period and offspring depression at age 18 years. We tested a hypothesized moderator (ie, sex) and conducted path analysis to examine hypothesized mediators (ie, depression in the other parent, couple conflict, and paternal involvement and emotional problems, conduct problems, and hyperactivity in offspring at age 3.5 years) of the associations between both paternal and maternal depression and offspring depression. Data collection for the Avon Longitudinal Study of Parents and Children began in 1991 and is ongoing. Data analysis for this study was conducted from June 2015 to September 2018. EXPOSURES: Depression symptoms in fathers at 8 weeks after the birth of their children. MAIN OUTCOMES AND MEASURES: Offspring depression symptoms at age 18 years, using International Statistical Classification of Diseases and Related Health Problems, Tenth Revision codes. RESULTS: A total of 3176 father-offspring pairs were analyzed; of the children, 1764 were girls (55.5%) and 1412 (44.5%) were boys. Paternal mean (SD) age at delivery was 29.6 (9.6) years. The offspring of fathers who had depression during the postnatal period were at increased risk of experiencing depression symptoms at age 18 years (β = 0.053 [95% CI, 0.02-0.09]). The association is mediated by maternal depression at 8 months after birth (β = 0.011 [95% CI, 0.0008-0.02]; 21% [0.011/0.053]) and conduct problems at 42 months after birth (β = 0.004; [95% CI , -0.00004 to 0.009]; 7.5% [0.004/0.053]). Couple conflict and paternal involvement do not mediate this association. The increased risk is seen in girls but not boys (interaction β = 0.095; P = .01). CONCLUSIONS AND RELEVANCE: The association between paternal depression in the postnatal period and depression in girls at age 18 years is partially explained by maternal depression. Couple conflict and paternal involvement were not found to play a role in the risk of transmission; this contrasts with the role that couple conflict was found to play in the risk of childhood behavior problems. Conduct problems in childhood appear to be a pathway for risk transmission between paternal depression and subsequent depression in offspring at age 18 years.