Evidence indicating abnormal functional connectivity (FC) among the cortex, thalamus, and cerebellum in schizophrenia patients has increased. However, the role of the thalamus and cerebellum when integrated into intrinsic networks and how those integrated networks interact in schizophrenia patients are largely unknown. We generated an integrative network map by merging thalamic and cerebellar network maps, which were parcellated using a winner-take-all approach, onto a cortical network map. Using cognitive networks, the default mode network (DMN), the dorsal attention network (DAN), the salience network (SAL), and the central executive network (CEN) as regions of interest, the FC of 48 schizophrenia patients was compared with that of 57 healthy controls (HCs). The association between abnormal FC and cognitive impairment was also investigated in patients. FC was lower between the SAL-CEN, SAL-DMN, and DMN-CEN and within-CEN in schizophrenia patients than in HCs. Hypoconnectivity between the DMN-CEN was correlated with impaired cognition in schizophrenia patients. Our findings broadly suggest the plausible role of the thalamus and cerebellum in integrative intrinsic networks in patients, which may contribute to the disrupted triple network and cognitive dysmetria in schizophrenia.