Heterogeneous Information Networks (HINs), which consist of various types of nodes and edges, have recently witnessed excellent performance in graph mining. However, most existing heterogeneous graph neural networks (HGNNs) fail to simultaneously handle the problems of missing attributes, inaccurate attributes and scarce node labels, which limits their expressiveness. In this paper, we propose a generative self-supervised model GraMI to address these issues simultaneously. Specifically, GraMI first initializes all the nodes in the graph with a low-dimensional representation matrix. After that, based on the variational graph autoencoder framework, GraMI learns both node-level and attribute-level embeddings in the encoder, which can provide fine-grained semantic information to construct node attributes. In the decoder, GraMI reconstructs both links and attributes. Instead of directly reconstructing raw features for attributed nodes, GraMI generates the initial low-dimensional representation matrix for all the nodes, based on which raw features of attributed nodes are further reconstructed. In this way, GraMI can not only complete informative features for non-attributed nodes, but rectify inaccurate ones for attributed nodes. Finally, we conduct extensive experiments to show the superiority of GraMI in tackling HINs with missing and inaccurate attributes. Our code and data can be found here: https://github.com/See-r/GraMI.