Advancements in micro-scale additive manufacturing techniques have made it possible to fabricate intricate architectures including 3D interpenetrating electrode microstructures. A mesoscale electrochemical lithium-ion battery model is presented and implemented in the PETSc software framework using a finite volume scheme. The model is used to investigate interpenetrating 3D electrode architectures that offer potential energy density and power density improvements over traditional particle bed battery geometries. Using the computational model, a variety of battery electrode geometries are simulated and compared across various battery discharge rates and length scales to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density vs. power density relationship of the electrode microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle-bed electrode designs are predicted, and electrode microarchitectures derived from minimal surfaces are shown to be superior under a minimum feature size constraint, especially when subjected to high discharge currents. An average Thiele modulus formulation is presented as a back-of-the-envelope calculation to predict the performance trends of microbattery electrode geometries. (C) The Author(s) 2019. Published by ECS.