Origin-Destination (OD) demand prediction is a pivotal yet highly challenging task in intelligent transportation systems, aiming to accurately forecast cross-region ridership flows within urban networks. While previous studies have focused on modeling node-to-node relationships, most of them neglect the fact that nodes (regions/stations) exhibit similar spatio-temporal (ST) patterns, which are termed as spatio-temporal prototypes. Capturing these prototypes is crucial for understanding the unified ST dependencies across the network. To bridge this gap, we propose STPro, an ST prototype-based hierarchical model with a dual-branch structure that extracts ST features from the micro and macro perspectives. At the micro level, our model learns unified ST features of individual nodes, while at the macro level, it employs dynamic clustering to identify city-wide ST prototypes, thereby uncovering latent patterns of urban mobility. Besides, we leverage different roles of nodes as origins and destinations by constructing dual O and D branches and learn the mutual information to model their intricate interactions and correlations. Extensive experiments on two public datasets demonstrate that our STPro outperforms recent state-of-the-art baselines, achieving remarkable predictive improvements in OD demand prediction.