Impressive milestones have been achieved in text matching by adopting a cross-attention mechanism to capture pertinent semantic connections between two sentences. However, these cross-attention mechanisms focus on word-level links between the two inputs, neglecting the importance of contextual information. We propose a context-aware interaction network (COIN) to properly align two sequences and infer their semantic relationship. Specifically, each interaction block includes (1) a context-aware cross-attention mechanism to effectively integrate contextual information, and (2) a gate fusion layer to flexibly interpolate aligned representations. We apply multiple stacked interaction blocks to produce alignments at different levels and gradually refine the attention results. Experiments on two question matching datasets and detailed analyses confirm the effectiveness of our model.