Background Previous studies have found significant associations between maternal prenatal and postpartum depression and child behavior problems (CBP). The present study investigates whether associations remain in a prospective, longitudinal design adjusted for familial confounding. Methods The sample comprised 11,599 families including 17,830 siblings from the Norwegian Mother and Child Cohort study. Mothers reported depressive symptoms at gestational weeks 17 and 30, as well as 6 months, 1.5, 3, and 5 years postpartum. Fathers’ depression was measured at gestational week 17. At the last three time‐points, child internalizing and externalizing problems were concurrently assessed. We performed multilevel analyses for internalizing and externalizing problems separately, using parental depression as predictors. Analyses were repeated using a sibling comparison design to adjust for familial confounding. Results All parental depressive time‐points were significantly and positively associated with child internalizing and externalizing problems. After sibling comparison, however, only concurrent maternal depression was significantly associated with internalizing [estimate = 2.82 (1.91–3.73, 95% CI)] and externalizing problems [estimate = 2.40 (1.56–3.23, 95% CI)]. The effect of concurrent maternal depression on internalizing problems increased with child age. Conclusions Our findings do not support the notion that perinatal maternal depression is particularly detrimental to children's psychological development, as the most robust effects were found for maternal depression occurring during preschool years.