Despite the successes of machine learning (ML) and deep learning (DL)-based vulnerability detectors (VD), they are limited to providing only the decision on whether a given code is vulnerable or not, without details on what part of the code is relevant to the detected vulnerability. We present IVDetect, an interpretable vulnerability detector with the philosophy of using Artificial Intelligence (AI) to detect vulnerabilities, while using Intelligence Assistant (IA) to provide VD interpretations in terms of vulnerable statements. For vulnerability detection, we separately consider the vulnerable statements and their surrounding contexts via data and control dependencies. This allows our model better discriminate vulnerable statements than using the mixture of vulnerable code and contextual code as in existing approaches. In addition to the coarse-grained vulnerability detection result, we leverage interpretable AI to provide users with fine-grained interpretations that include the sub-graph in the Program Dependency Graph (PDG) with the crucial statements that are relevant to the detected vulnerability. Our empirical evaluation on vulnerability databases shows that IVDetect outperforms the existing DL-based approaches by 43%-84% and 105%-255% in top-10 nDCG and MAP ranking scores. IVDetect correctly points out the vulnerable statements relevant to the vulnerability via its interpretation in 67% of the cases with a top-5 ranked list. IVDetect improves over the baseline interpretation models by 12.3%-400% and 9%-400% in accuracy.