Heterogeneous information networks(HINs) become popular in recent years for its strong capability of modelling objects with abundant information using explicit network structure. Network embedding has been proved as an effective method to convert information networks into lower-dimensional space, whereas the core information can be well preserved. However, traditional network embedding algorithms are sub-optimal in capturing rich while potentially incompatible semantics provided by HINs. To address this issue, a novel meta-path-based HIN representation learning framework named mSHINE is designed to simultaneously learn multiple node representations for different meta-paths. More specifically, one representation learning module inspired by the RNN structure is developed and multiple node representations can be learned simultaneously, where each representation is associated with one respective meta-path. By measuring the relevance between nodes with the designed objective function, the learned module can be applied in downstream link prediction tasks. A set of criteria for selecting initial meta-paths is proposed as the other module in mSHINE which is important to reduce the optimal meta-path selection cost when no prior knowledge of suitable meta-paths is available. To corroborate the effectiveness of mSHINE, extensive experimental studies including node classification and link prediction are conducted on five real-world datasets. The results demonstrate that mSHINE outperforms other state-of-the-art HIN embedding methods.