As a manifestation of the molecular Aharonov-Bohm effect, tunneling-facilitated dissociation under a conical intersection (CI) requires the inclusion of the geometric phase (GP) to ensure a single-valued adiabatic wave function encircling the CI. In this work, we demonstrate using a simple two-dimensional model that the GP induces destructive interference for vibrational states with even quanta in the coupling mode, but it leads to constructive interference for those with odd quanta. The interference patterns are manifested in tunneling wave functions and clearly affect the tunneling lifetime. It is further shown that the inclusion of the diagonal Born-Oppenheimer correction is necessary for agreement with exact results.