Composite waveplates consisting of two or more single waveplates are widely used in optical instruments, such as ellipsometry, polarimetry, cryptography, and photoelasticity. Accurate calibration of the misalignment errors in composite waveplates is of great importance (to minimize or correct the spurious artifacts in the final collected spectral data of these instruments induced by the misalignment errors). In this paper, we choose the fast axis azimuth and the rotary angle of composite waveplates as the detected characteristic parameters to calibrate the misalignment errors in composite waveplates. We first derive a general analytical model to describe the relationship between the mislignment errors and the characteristic parameters, and then propose an inverse approach to the calibration of the misalignment errors in composite waveplates. An experimental device based on the dual rotating-compensator Mueller matrix ellipsometry principle is set up to measure the characteristic parameters of composite waveplates. Both numerical simulations and experiments on an MgF(2)-MgF(2)-quartz triplate demonstrate the correctness and efficiency of the proposed approach. It is expected that the proposed approach can be readily extended to calibrate the misalignment errors in more complex composite waveplates.