To understand temporally extended events, the human brain needs to accumulate information continuously across time. Interruptions that require switching of attention to other event sequences disrupt this process. To reveal neural mechanisms supporting integration of event information, we measured brain activity with functional magnetic resonance imaging (fMRI) from 18 participants while they viewed 6.5-minute excerpts from three movies (i) consecutively and (ii) as interleaved segments of approximately 50-s in duration. We measured inter-subject reliability of brain activity by calculating inter-subject correlations (ISC) of fMRI signals and analyzed activation timecourses with a general linear model (GLM). Interleaving decreased the ISC in posterior temporal lobes, medial prefrontal cortex, superior precuneus, medial occipital cortex, and cerebellum. In the GLM analyses, posterior temporal lobes were activated more consistently by instances of speech when the movies were viewed consecutively than as interleaved segments. By contrast, low-level auditory and visual stimulus features and editing boundaries caused similar activity patterns in both conditions. In the medial occipital cortex, decreases in ISC were seen in short bursts throughout the movie clips. By contrast, the other areas showed longer-lasting differences in ISC during isolated scenes depicting socially-relevant and suspenseful content, such as deception or inter-subject conflict. The areas in the posterior temporal lobes also showed sustained activity during continuous actions and were deactivated when actions ended at scene boundaries. Our results suggest that the posterior temporal and dorsomedial prefrontal cortices, as well as the cerebellum and dorsal precuneus, support integration of events into coherent event sequences.