Hall probe microscopy has been used to image vortex-antivortex molecules induced in superconducting Pb films by the stray fields from square arrays of magnetic dots. We have directly observed spontaneous vortex-antivortex pairs and studied how they interact with added free (anti)fluxons in an applied magnetic field. We observe a variety of phenomena arising from competing symmetries which either drive added antivortices to join antivortex shells around dots or stabilize the translationally symmetric antivortex lattice between the dots. Added vortices annihilate antivortex shells, leading first to a stable “nulling state” with no free fluxons and then, at high densities, to vortex shells around the dots stabilized by the asymmetric antipinning potential. Our experimental findings are in good agreement with Ginzburg-Landau calculations.