Naturalistic stimuli evoke complex neural responses with spatial and temporal properties that differ across individuals. Current alignment methods focus on either spatial hyperalignment (assuming exact temporal correspondence) or temporal alignment (assuming exact spatial correspondence). Here, we propose a hybrid model, the Hyper-HMM, that simultaneously aligns both temporal and spatial features across brains. The model learns to linearly project voxels to a reduced-dimension latent space, in which timecourses are segmented into corresponding temporal events. This approach allows tracking of each individual's mental trajectory through an event sequence, and also allows for alignment with other feature spaces such as stimulus content. Using an fMRI dataset in which students watch videos of class lectures, we demonstrate that the Hyper-HMM can be used to map all participants and the semantic content of the videos into a common low-dimensional space, and that these mappings generalize to held-out data. Our model provides a new window into individual cognitive dynamics evoked by complex naturalistic stimuli.