Genetic susceptibility factors behind psychiatric disorders typically contribute small effects individually. A possible explanation for the missing heritability is that the effects of common variants are not only polygenic but also non-additive, appearing only when interactions within large groups are taken into account. Here, we tested this hypothesis for schizophrenia (SZ) and bipolar disorder (BP) disease risks, and identified genetic factors shared with posttraumatic stress disorder (PTSD). When considered independently, few single-nucleotide polymorphisms (SNPs) reached genome-wide significance. In contrast, when SNPs were selected in groups (containing up to thousands each) and the collective effects of all interactions were estimated, the association strength for SZ/BP rose dramatically with a combined sample size of 7187 cases and 8309 controls. We identified a large number of genes and pathways whose association was significant only when interaction effects were included. The gene with highest association was CSMD1, which encodes a negative regulator of complement activation. Pathways for glycosaminoglycan (GAG) synthesis exhibited strong association in multiple contexts. Taken together, highly associated pathways suggested a pathogenesis mechanism where maternal immune activation causes disruption of neurogenesis (compounded by impaired cell cycle, DNA repair and neuronal migration) and deficits in cortical interneurons, leading to symptoms triggered by synaptic pruning. Increased risks arise from GAG deficiencies causing complement activation and excessive microglial action. Analysis of PTSD data sets suggested an etiology common to SZ/BP: interneuron deficiency can also lead to impaired control of fear responses triggered by trauma. We additionally found PTSD risk factors affecting synaptic plasticity and fatty acid signaling, consistent with the fear extinction model. Our results suggest that much of the missing heritability of psychiatric disorders resides in non-additive interaction effects.