Deep network-based image and video Compressive Sensing(CS) has attracted increasing attentions in recent years. However, in the existing deep network-based CS methods, a simple stacked convolutional network is usually adopted, which not only weakens the perception of rich contextual prior knowledge, but also limits the exploration of the correlations between temporal video frames. In this paper, we propose a novel Hierarchical InTeractive Video CS Reconstruction Network(HIT-VCSNet), which can cooperatively exploit the deep priors in both spatial and temporal domains to improve the reconstruction quality. Specifically, in the spatial domain, a novel hierarchical structure is designed, which can hierarchically extract deep features from keyframes and non-keyframes. In the temporal domain, a novel hierarchical interaction mechanism is proposed, which can cooperatively learn the correlations among different frames in the multiscale space. Extensive experiments manifest that the proposed HIT-VCSNet outperforms the existing state-of-the-art video and image CS methods in a large margin.