Instrument-tissue interaction detection task, which helps understand surgical activities, is vital for constructing computer-assisted surgery systems but with many challenges. Firstly, most models represent instrument-tissue interaction in a coarse-grained way which only focuses on classification and lacks the ability to automatically detect instruments and tissues. Secondly, existing works do not fully consider relations between intra-and inter-frame of instruments and tissues. In the paper, we propose to represent instrument-tissue interaction as ⟨instrument class, instrument bounding box, tissue class, tissue bounding box, action class⟩ quintuple and present an Instrument-Tissue Interaction Detection Network (ITIDNet) to detect the quintuple for surgery videos understanding. Specifically, we propose a Snippet Consecutive Feature (SCF) Layer to enhance features by modeling relationships of proposals in the current frame using global context information in the video snippet. We also propose a Spatial Corresponding Attention (SCA) Layer to incorporate features of proposals between adjacent frames through spatial encoding. To reason relationships between instruments and tissues, a Temporal Graph (TG) Layer is proposed with intra-frame connections to exploit relationships between instruments and tissues in the same frame and inter-frame connections to model the temporal information for the same instance. For evaluation, we build a cataract surgery video (PhacoQ) dataset and a cholecystectomy surgery video (CholecQ) dataset. Experimental results demonstrate the promising performance of our model, which outperforms other state-of-the-art models on both datasets.