This work proposes and analyzes a structurally-integrated lithium-ion battery concept. The multifunctional energy storage composite (MESC) structures developed here encapsulate lithium-ion battery materials inside high-strength carbon-fiber composites and use interlocking polymer rivets to stabilize the electrode layer stack mechanically. These rivets enable load transfer between battery layers, allowing them to store electrical energy while also contributing to the structural load carrying performance, without any modifications to the battery chemistry. The design rationale, fabrication processes, and experimental mechano-electrical characterization of first-generation MESCs are discussed. Experimental results indicate that the MESCs offer electrochemical performance comparable to standard lithium-ion cells, despite the disruptive design change. The mechanical performance of MESCs is assessed via quasi-static three-point bending tests, with results showing significantly improved mechanical stiffness and strength over traditional pouch cells. The rivets minimize interlayer shear movement of the electrode stack, thus allowing it to maintain electrochemical functionalities while carrying mechanical bending. While minimal load application can cause permanent deformation of pouch cells, MESCs maintain their structural integrity and energy-storage capabilities under realistic repeated loading. The results obtained demonstrate the mechanical robustness of MESCs, which allow them to be fabricated as energy-storing structures for electric vehicles and other applications.