Event cameras have shown promise in vision applications like optical flow estimation and stereo matching, with many specialized architectures leveraging the asynchronous and sparse nature of event data. However, existing works only focus event data within the confines of task-specific domains, overlooking how tasks across the temporal and spatial domains can reinforce each other. In this paper, we reformulate event-based flow estimation and stereo matching as a unified dense correspondence matching problem, enabling us to solve both tasks within a single model by directly matching features in a shared representation space. Specifically, our method utilizes a Temporal Recurrent Network to aggregate event features across temporal or spatial domains, and a Spatial Contextual Attention to enhance knowledge transfer across event flows via temporal or spatial interactions. By utilizing a shared feature similarities module that integrates knowledge from event streams via temporal or spatial interactions, our network performs optical flow estimation from temporal event segment inputs and stereo matching from spatial event segment inputs simultaneously. We demonstrate that our unified model inherently supports multi-task fusion and cross-task transfer. Without the need for retraining for specific task, our model can effectively handle both optical flow and stereo estimation, achieving state-of-the-art performance on both tasks.