Chinese Medical Named Entity Recognition (Chinese-MNER) aims to identify potential entities and their categories from the unstructured Chinese medical text. Existing methods for this task mainly incorporate the dictionary knowledge on the basis of traditional BiLSTM-CRF or BERT architecture. However, the construction of high-quality dictionaries is typically time consuming and labor-intensive, which may also damage the robustness of NER models. What is more, the limited amount of annotated Chinese-MNER data can easily lead to the over-fitting problem while training. With the aim of dealing with the above problems, we put forward a BERT-BiLSTM-CRF model by integrating the part-of-speech (POS) tagging features and a Regularization method (BBCPR) for Chinese-MNER. In BBCPR, we first leverage a POS fusion layer to incorporate external syntax knowledge. Next, we design a novel REgularization mothod with Adversarial training and Dropout (READ) to improve the model robustness. Specifically, READ focuses on reducing the difference between the predictions of two sub-models through minimizing the bidirectional KL divergence between the adversarial output and original output distributions for the same sample. Comprehensive evaluations on two public data sets, namely, cMedQANER and cEHRNER from the Chinese Biomedical Language Understanding Evaluation benchmark (ChineseBLUE), demonstrate the superiority of our proposal in Chinese-MNER. In addition, ablation study shows that READ can effectively improve the model performance. Our proposal does well in exploring the technical terms and identifying the word boundary.