Individuals with schizophrenia (SZ) or bipolar disorder (BP) display cognitive impairments, while their first-degree relatives perform at an intermediate level between the patient groups and controls. However, the environmental impact of having an ill relative likely varies with the type of kinship and some studies suggest that offspring may be particularly disadvantaged. The present study aimed to investigate the relationship between parent and child cognition in parents with SZ or BD and their 7-year-old offspring. A population-based cohort of 522 children (parental SZ, n = 202; parental BP, n = 120; controls, n = 200) and their parents underwent the same assessment battery covering a wide range of cognitive functions. We used Bayesian statistics to model performance. We found that performance on non-verbal tests was better in offspring than parents with SZ or BP, using the controls as reference. However, for verbal tests, there was little to no evidence for this pattern or even some evidence for the opposite in the BP group: relatively better performance in parents than offspring. The findings suggest that the offspring of parents with SZ or BP may be particularly disadvantaged in verbal abilities. Future studies will show whether this pattern persists throughout development.