We present a theoretical and experimental analysis of the cantilever motions detected in photoinduced force microscopy (PiFM) using the sideband coupling detection scheme. In sideband coupling, the cantilever dynamics are probed at a combination frequency of a fundamental mechanical eigenmode and the modulation frequency of the laser beam. Using this detection mode, we develop a method for reconstructing the modulated photo-induced force gradient from experimental parameters in a quantitative manner. We show evidence, both theoretically and experimentally, that the sideband coupling detection mode provides PiFM images with superior contrast compared to images obtained when detecting the cantilever motions directly at the laser modulation frequency.