Deep learning has recently been widely applied to many applications across different domains, e.g., image classification and audio recognition. However, the quality of Deep Neural Networks (DNNs) still raises concerns in the practical operational environment, which calls for systematic testing, especially in safety-critical scenarios. Inspired by software testing, a number of structural coverage criteria are designed and proposed to measure the test adequacy of DNNs. However, due to the blackbox nature of DNN, the existing structural coverage criteria are difficult to interpret, making it hard to understand the underlying principles of these criteria. The relationship between the structural coverage and the decision logic of DNNs is unknown. Moreover, recent studies have further revealed the non-existence of correlation between the structural coverage and DNN defect detection, which further posts concerns on what a suitable DNN testing criterion should be. In this paper, we propose the interpretable coverage criteria through constructing the decision structure of a DNN. Mirroring the control flow graph of the traditional program, we first extract a decision graph from a DNN based on its interpretation, where a path of the decision graph represents a decision logic of the DNN. Based on the control flow and data flow of the decision graph, we propose two variants of path coverage to measure the adequacy of the test cases in exercising the decision logic. The higher the path coverage, the more diverse decision logic the DNN is expected to be explored. Our large-scale evaluation results demonstrate that: the path in the decision graph is effective in characterizing the decision of the DNN, and the proposed coverage criteria are also sensitive with errors including natural errors and adversarial examples, and strongly correlated with the output impartiality.