This paper summarizes eight design requirements for DNN testing criteria, taking into account distribution properties and practical concerns. We then propose a new criterion, NLC, that satisfies all of these design requirements. NLC treats a single DNN layer as the basic computational unit (rather than a single neuron) and captures four critical features of neuron output distributions. Thus, NLC is denoted as NeuraL Coverage, which more accurately describes how neural networks comprehend inputs via approximated distributions rather than neurons. We demonstrate that NLC is significantly correlated with the diversity of a test suite across a number of tasks (classification and generation) and data formats (image and text). Its capacity to discover DNN prediction errors is promising. Test input mutation guided by NLC result in a greater quality and diversity of exposed erroneous behaviors.