A heterogeneous information network (HIN) has as vertices objects of different types and as edges the relations between objects, which are also of various types. We study the problem of classifying objects in HINs. Most existing methods perform poorly when given scarce labeled objects as training sets, and methods that improve classification accuracy under such scenarios are often computationally expensive. To address these problems, we propose ConCH, a graph neural network model. ConCH formulates the classification problem as a multi-task learning problem that combines semi-supervised learning with self-supervised learning to learn from both labeled and unlabeled data. ConCH employs meta-paths, which are sequences of object types that capture semantic relationships between objects. Based on meta-paths, it considers two sources of information for an object x: (1) Meta-path-based neighbors of x are retrieved and ranked, and the top-k neighbors are retained. (2) The meta-path instances of x to its selected neighbors are used to derive meta-path-based contexts. ConCH utilizes the above information to co-derive object embeddings and context embeddings via graph convolution. It also uses the attention mechanism to fuse the embeddings of x generated from various meta-paths to obtain x's final embedding. We conduct extensive experiments to evaluate the performance of ConCH against other 14 classification methods. Our results show that ConCH is an effective and efficient method for HIN classification.