The goal of network embedding is to transform nodes in a network to a low-dimensional embedding space. Recently, heterogeneous network has shown to be effective in representing diverse information in data. However, heterogeneous network embedding suffers from the imbalanced property, i.e. the number of relation types is imbalanced. In this paper, we devise a new heterogeneous network embedding method, called BHIN2vec, which considers the balance among all relationships in a network. We view the heterogeneous network embedding as simultaneously solving multiple tasks in which each task corresponds to each relation type in a network. After splitting the skip-gram loss into multiple losses corresponding to different tasks, we propose a novel random-walk strategy to focus on the tasks with high loss values by considering relative training ratio. Unlike previous random walk strategy, our proposed random walk strategy generates training samples according to the relative training ratio among different tasks, which results in a balanced training of the node embeddings. Our extensive experiments on node classification and recommendation demonstrate the superiority of BHIN2vec compared with several state-of-the-art methods. Also, based on the relative training ratio, we analyze how much each relation type is represented in the embedding space during training.