Although lithium metal anodes are expected to increase the energy density of next-generation batteries, dendrite growth during charge remains a major bottleneck preventing widespread implementation. Composite solid electrolytes with ceramic particles embedded in a polymer matrix have the potential to prevent dendrites owing to the higher mechanical stiffness while also possessing the flexibility to maintain contact with the electrode. However, microscopically, the different mechanical and electrochemical properties of the polymer and ceramic domains can cause inhomogeneous charge transfer at the Li/electrolyte interface, which can lead to nonuniform Li deposition and propagation of dendrites. Here, we computationally examine the coupled electrochemical, transport, and mechanical processes at the interface to determine the propensity for dendrite formation and possible approaches to mitigate this issue. Predictions of two possible microstructures at the interface, namely, (i) where both the polymer and ceramic come in contact with Li metal and (ii) when only the polymer comes in contact with Li metal, suggest that the former has a greater tendency for nonuniform plating. In addition, predictions suggest that minimizing the interfacial resistance between polymers and ceramics and incorporating interlayers between the electrode and electrolyte help mitigate current heterogeneity. These predictions provide guidance for experimental approaches to prevent dendrites in composite electrolytes.