Multimodal brain networks characterize complex connectivities among different brain regions from both structural and functional aspects and provide a new means for mental disease analysis. Recently, Graph Neural Networks (GNNs) have become a de facto model for analyzing graph-structured data. However, how to employ GNNs to extract effective representations from brain networks in multiple modalities remains rarely explored. Moreover, as brain networks provide no initial node features, how to design informative node attributes and leverage edge weights for GNNs to learn is left unsolved. To this end, we develop a novel multiview GNN for multimodal brain networks. In particular, we treat each modality as a view for brain networks and employ contrastive learning for multimodal fusion. Then, we propose a GNN model which takes advantage of the message passing scheme by propagating messages based on degree statistics and brain region connectivities. Extensive experiments on two real-world disease datasets (HIV and Bipolar) demonstrate the effectiveness of our proposed method over state-of-the-art baselines.