The existing emotion-cause pair extraction (ECPE) task, unfortunately, ignores extracting the emotion type and cause type, while these fine-grained meta-information can be practically useful in real-world applications, i.e., chat robots and empathic dialog generation. Also the current ECPE is limited to the scenario of single text piece, while neglecting the studies at dialog level that should have more realistic values. In this paper, we extend the ECPE task with a broader definition and scenario, presenting a new task, Emotion-Cause Quadruple Extraction in Dialogs (ECQED), which requires detecting emotion-cause utterance pairs and emotion and cause types. We present an ECQED model based on a structural and semantic heterogeneous graph as well as a parallel grid tagging scheme, which advances in effectively incorporating the dialog context structure, meanwhile solving the challenging overlapped quadruple issue. Via experiments we show that introducing the fine-grained emotion and cause features evidently helps better dialog generation. Also our proposed ECQED system shows exceptional superiority over baselines on both the emotion-cause quadruple or pair extraction tasks, meanwhile being highly efficient.