Multigraphs with heterogeneous views present one of the most challenging obstacles to classification tasks due to their complexity. Several works based on feature selection have been recently proposed to disentangle the problem of multigraph heterogeneity. However, such techniques have major drawbacks. First, the bulk of such works lies in the vectorization and the flattening operations, failing to preserve and exploit the rich topological properties of the multigraph. Second, they learn the classification process in a dichotomized manner where the cascaded learning steps are pieced in together independently. Hence, such architectures are inherently agnostic to the cumulative estimation error from step to step. To overcome these drawbacks, we introduce MICNet (multigraph integration and classifier network), the first end-to-end graph neural network based model for multigraph classification. First, we learn a single-view graph representation of a heterogeneous multigraph using a GNN based integration model. The integration process in our model helps tease apart the heterogeneity across the different views of the multigraph by generating a subject-specific graph template while preserving its geometrical and topological properties conserving the node-wise information while reducing the size of the graph (i.e., number of views). Second, we classify each integrated template using a geometric deep learning block which enables us to grasp the salient graph features. We train, in end-to-end fashion, these two blocks using a single objective function to optimize the classification performance. We evaluate our MICNet in gender classification using brain multigraphs derived from different cortical measures. We demonstrate that our MICNet significantly outperformed its variants thereby showing its great potential in multigraph classification.