Geometric stochastic resonance of particles diffusing across a porous membrane subject to oscillating forces is characterized as a synchronization process. Noninteracting particle currents through a symmetric membrane pore are driven either perpendicular or parallel to the membrane, whereas, harmonic-mixing spectral current components are generated by the combined action of perpendicular and parallel drives. In view of potential applications to the transport of colloids and biological molecules through narrow pores, we also consider the role of particle repulsion as a controlling factor.