Location-based service networks (LBSNs) have emerged as a primary source for numerous applications that attempt to understand human mobility and analyze social networks. However, mainstream studies on representation learning often consider LBSNs to be either regular graphs or a mixture of regular graphs and hypergraphs. As a potential solution, hypergraph convolution has recently emerged as a way to capture the structural context of hypergraphs. But applying this type of convolution to representation learning in an LBSN is challenging due to the inherent heterogeneity of LSBNs. In this paper, we address the inherent heterogeneity of LBSNs and enhance the performance of representation learning by leveraging the power of multi-task learning. By jointly optimizing both friendship prediction and POI recommendation tasks, our proposed framework, MH2-LBSN, effectively leverages the complementary information present in these tasks to learn more informative and robust representations. Extensive experiments with four real-world datasets against several state-of-the-art embedding methods validate the performance of MH2-LBSN.