Heterogeneous information networks (HINs) are ubiquitous in real-world applications. Due to the heterogeneity in HINs, the typed edges may not fully align with each other. In order to capture the semantic subtlety, we propose the concept of aspects with each aspect being a unit representing one underlying semantic facet. Meanwhile, network embedding has emerged as a powerful method for learning network representation, where the learned embedding can be used as features in various downstream applications. Therefore, we are motivated to propose a novel embedding learning framework---AspEm---to preserve the semantic information in HINs based on multiple aspects. Instead of preserving information of the network in one semantic space, AspEm encapsulates information regarding each aspect individually. In order to select aspects for embedding purpose, we further devise a solution for AspEm based on dataset-wide statistics. To corroborate the efficacy of AspEm, we conducted experiments on two real-words datasets with two types of applications---classification and link prediction. Experiment results demonstrate that AspEm can outperform baseline network embedding learning methods by considering multiple aspects, where the aspects can be selected from the given HIN in an unsupervised manner.