Grand canonical Monte Carlo calculations are used to investigate the phase behavior of a binary mixture of Lennard-Jones particles confined between planar, parallel, chemically patterned plates. Attention is focused on the influence of surface-induced transitions on the net force acting between the plates. In addition to the stable and metastable bulk states that play a crucial role for homogeneous surfaces, for certain patterns and surface separations a bridge phase analogous to that recently reported for one-component systems is observed. It is found that bridge phase formation leads to strongly attractive plate-plate forces that are equal in magnitude to those observed for homogeneous surfaces. The significance of our results for the interaction and behavior of nonuniform macroparticles in solution is discussed.