Locally resonant metamaterials are characterized by bandgaps at wavelengths much larger than the lattice size, which enables low-frequency vibration attenuation in structures. Next-generation metastructures (i.e. finite metamaterial-based structures) hosting mechanical resonators as well as piezoelectric interfaces connected to resonating circuits enable the formation of two bandgaps, right above and below the design frequency of the mechanical and electrical resonators, respectively. This new class of hybrid metastructures proposed in this work can therefore exhibit a wider bandgap size and enhanced design flexibility as compared to using a purely mechanical, or a purely electromechanical metastructure alone. To this end, we bridge our efforts on modal analysis of mechanical and electromechanical locally resonant metastructures and establish a fully coupled framework for hybrid mechanical-electromechanical metastructures. Combined bandgap size is approximated in closed form for sufficient number of mechanical and electromechanical resonators. Case studies are presented to understand the interaction of these two locally resonating metastructure domains in bandgap formation, and conclusions are drawn for design and optimization of such hybrid metastructures. Numerical results from modal analysis are compared with dispersion analysis using the plane wave expansion method and the proposed analytical framework is validated succesfully.