Binocular disparity signals can provide high acuity information about the positions of points, surfaces, and objects in three-dimensional space. For some stimulus configurations, however, perceived depth is known to be affected by surface organization. Here we examine the effects of surface continuity and discontinuity on such surface organization biases. Participants were presented with a series of random dot surfaces, each with a cumulative Gaussian form in depth. Surfaces varied in the steepness of disparity gradients, via manipulation of the standard deviation of the Gaussian, and/or the presence of differing forms of surface discontinuity. By varying the relative disparity between surface edges, we measured the points of subjective equality, where surfaces of differing steepness and/or discontinuity were perceptually indistinguishable. We compare our results to a model that considers sensitivity to different frequencies of disparity modulation. Across a series of experiments, the observed patterns of change in points of subjective equality suggest that perceived depth is determined by the integration of measures of relative disparity, with a bias toward sharp changes in disparity. Such disparities increase perceived depth when they are in the same direction as the overall disparity. Conversely, perceived depth is reduced by the presence of sharp disparity changes that oppose the sign of the overall depth change.