Understanding the relationship between behavior and neural activity is crucial for understanding brain function. One effective method is to learn embeddings for interconnected modalities. For simple behavioral tasks, neural features can be learned based on labels. However, complex behavioral tasks and social behaviors require joint extraction of both behavioral and neural features. In this paper, we present an autoencoder (AE) framework, called Shared-AE, which includes a novel regularization term that automatically identifies features shared between neural activity and behavior, while simultaneously capturing the unique private features specific to each modality. We apply Shared-AE, to large-scale neural activity recorded across the entire dorsal cortex of the mouse, during two very different behaviors: (i) head-fixed mice performing a self-initiated decision-making task, and (ii) freely-moving social behavior amongst two mice. Our model successfully captures both 'shared features', shared across the neural and behavioral activity, and 'private features', unique to each modality, significantly enhancing our understanding of the alignment between neural activity and complex behaviors. The original code for the entire Shared-AE framework on Pytorch has been made public at: https://github.com/saxenalab-neuro/Shared-AE.