Joint entity and relation extraction framework constructs a unified model to perform entity recognition and relation extraction simultaneously, which can exploit the dependency between the two tasks to mitigate the error propagation problem suffered by the pipeline model. Current efforts on joint entity and relation extraction focus on enhancing the interaction between entity recognition and relation extraction through parameter sharing, joint decoding, or other ad-hoc tricks (e.g., modeled as a semi-Markov decision process, cast as a multi-round reading comprehension task). However, there are still two issues on the table. First, the interaction utilized by most methods is still weak and uni-directional, which is unable to model the mutual dependency between the two tasks. Second, relation triggers are ignored by most methods, which can help explain why humans would extract a relation in the sentence. Theyre essential for relation extraction but overlooked. To this end, we present a Trigger-Sense Memory Flow Framework (TriMF) for joint entity and relation extraction. We build a memory module to remember category representations learned in entity recognition and relation extraction tasks. And based on it, we design a multi-level memory flow attention mechanism to enhance the bi-directional interaction between entity recognition and relation extraction. Moreover, without any human annotations, our model can enhance relation trigger information in a sentence through a trigger sensor module, which improves the model performance and makes model predictions with better interpretation. Experiment results show that our proposed framework achieves state-of-the-art results by improves the relation F1 to 52.44% (+3.2%) on SciERC, 66.49% (+4.9%) on ACE05, 72.35% (+0.6%) on CoNLL04 and 80.66% (+2.3%) on ADE.