Optical three-dimensional (3D) topography measurement technology has been widely used in different fields because of its non-destructive, rapid, high precision, and other advantages. Rapid and accurate measurements of the 3D morphology of specular/diffuse composite surfaces in industrial production have been an unsolved problem. In this study, a method for specular/diffuse composite surface measurements based on fringe projection and dual-screen transmission display is proposed, and the nonlinear response of the system is compensated. First, the normal and transparent screens display green stripes, which are partially reflected by the mirror. In addition, the projector projects a blue sinusoidal stripe pattern to the diffuse part. Second, the camera captures the deformed fringe patterns of different colors. Subsequently, the system parameters are obtained via 3D calibration, and the 3D morphology of the object is recovered based on the relationship between phase and depth. Finally, the nonlinear response error of the system is corrected and compensated to improve the accuracy of 3D measurements. The experimental results show that the proposed method can achieve high-precision measurements of the 3D topography for discontinuous composite surface objects.