Brain functional connectivity analysis is important for understanding brain development and brain disorders. Recent studies have suggested that the variations of functional connectivity among multiple subnetworks are closely related to the development of diseases. However, the existing works failed to sufficiently capture the complex correlation patterns among the subnetworks and ignored the learning of heterogeneous structural information across the subnetworks. To address these issues, we formulate a new paradigm for constructing and analyzing high-order heterogeneous functional brain networks via meta-paths and propose a Heterogeneous Graph representation Learning framework (BrainHGL). Our framework consists of three key aspects: 1) Meta-path encoding for capturing rich heterogeneous topological information, 2) Meta-path interaction for exploiting complex association patterns among subnetworks and 3) Meta-path aggregation for better meta-path fusion. To the best of our knowledge, we are the first to formulate the heterogeneous brain networks for better exploiting the relationship between the subnetwork interactions and the mental disease We evaluate BrainHGL on the private center Nanjing Medical University dataset (center NMU) and the public Autism Brain Imaging Data Exchange (ABIDE) dataset. We demonstrate the effectiveness of the proposed model across various disease classification tasks, including major depression disorder (MDD), bipolar disorder (BD) and autism spectrum disorder (ASD) diagnoses. In addition, our model provides deeper insights into disease interpretability, including the critical brain subnetwork connectivities, brain regions and functional pathways. We also identified disease subtypes consistent with previous neuroscientific studies by our model, which benefits the disease identification performance. The code is available at https://github.com/IntelliDAL/Graph/BrainHGL.