Due to the heterogeneity of nodes and edges, heterogeneous network embedding is a very challenging task to embed highly coupled networks into a set of low-dimensional vectors. Existing models either only learn embedding vectors for nodes or only for edges. These two methods of embedding learning are rarely performed in the same model, and they both overlook the internal correlation between nodes and edges. To solve these problems, a node and edge joint embedding model is proposed for Heterogeneous Information Networks (HINs), called NEJE. The NEJE model can better capture the latent structural and semantic information from an HIN through two joint learning strategies: type-level joint learning and element-level joint learning. Firstly, node-type-aware structure learning and edge-type-aware semantic learning are sequentially performed on the original network and its line graph to get the initial embedding of nodes and the embedding of edges. Then, to optimize performance, type-level joint learning is performed through the alternating training of node embedding on the original network and edge embedding on the line graph. Finally, a new homogeneous network is constructed from the original heterogeneous network, and the graph attention model is further used on the new network to perform element-level joint learning. Experiments on three tasks and five public datasets show that our NEJE model performance improves by about 2.83% over other models, and even improves by 6.42% on average for the node clustering task on Digital Bibliography & Library Project (DBLP) dataset.