Construction of bioinspired vasculature in synthetic materials enables multi-functional performance via mass transport through internal fluidic networks. However, exact reproduction of intricate, natural microvascular architectures is nearly impossible and thus there is a need to create practical, manufacturable designs guided by multi-physics principles. Here we present a Hybrid Topology/Shape (HyTopS) optimization scheme for microvascular materials using the Interface-enriched Generalized Finite Element Method (IGFEM). This new approach, which can simultaneously perform topological changes as well as shape optimization of microvascular materials, is demonstrated in the context of thermal regulation. In the current study, we present a new feature that enables the optimizer to augment network topology by creating/removing microchannels during the shape optimization process. This task has been accomplished by introducing a new set of design parameters, which act analogous to the penalization factor in the Solid Isotropic Material with Penalization (SIMP) method. The analytical sensitivity for the HyTopS optimization scheme has been derived and the sensitivity accuracy is verified against the finite difference method. We impose a set of geometrical constraints to account for manufacturing limitations and produce a design which is suitable for large-scale production without the need to perform post-processing on the obtained optimum. The method is validated by active-cooling experiments on vascularized carbon-fiber composites. Finally, we compare various application examples to demonstrate the advantages of the newly introduced HyTopS optimization scheme over solely shape optimization for microvascular materials.