Predicting treatment medicines is a key aspect of many intelligent healthcare systems. It's a very challenging task due to the following reasons: (1) heterogeneous nature of EHR data that typically include laboratory results, treatment medicines, disease conditions, and demographic details collected from disparate sources; (2) complex correlations among medical sequences, including inter-correlations between sequences and temporal intra-correlations within each sequence; (3) temporal diversity of these correlations, which is highly affected by changing disease progression. We proposes a dual adaptive sequential network, entitled DASNet, to dynamically predict treatment medicines for patients. Specifically, DASNet comprises the following three components. Decomposed Adaptive Long Short-Term Memory network (DA-LSTM) is designed to capture the intra- and inter-correlations in multiple heterogeneous temporal sequences. Then, we develop an Attentive Meta learning Network (AT-MetaNet), which produces location- and context-specific dynamic weight parameters for DA-LSTM, thus enabling it to model the time-varying multi-level correlations. Finally, we employ an ATtentive Fusion Network (AT-FuNet) to retrieve historical information and collectively fuse heterogeneous data representation embeddings to predict treatment medicines. The results of extensive experiments on the public MIMIC-III dataset covering 11 medical conditions demonstrate that the proposed end-to-end model can achieve the state-of-the-art prediction performance while providing clinically useful insights.