A bilayer composite electrolyte comprising BaCe_0.85Y_0.15O_3-d (BCY15) – Gd_0.2Ce_0.8O_2-d (GDC20) at the anode side and BaZr_0.85Y_0.15O_3-d (BZY15) – Nd_0.1Ce_0.9O_2-d (NDC10) at the cathode side is designed for improving the stability of co-ionic conducting solid oxide fuel cells (SOFCs) in a cell imbalanced stack. Contrary to the single layer structured SOFCs, the bi-layer cell stably operates without electrode delamination under negative voltage conditions. We measure local internal $p_{O_2}$ values using embedded Pt probes. Based on these values, local electronic conduction is estimated in combination with four probe DC conductivity measurements. It is found that n-type conductivity (∼10⁻³ Scm⁻¹) and p-type conductivity (10⁻⁵–10⁻⁴ Scm⁻¹) are developed in the BCY15-GDC20 near the anode side and in the BZY15-NDC10 near the cathode side, respectively. The results indicate that local electronic conduction in electrolyte regions near both the anode and cathode interfaces is a crucial factor for the durability of co-ionic SOFCs under negative voltage operation. We therefore suggest the bi-layer configuration as a practical solution to protect co-ionic SOFCs in a cell-imbalanced stack.