A refined two-dimensional formulation is presented for the static and free vibration analysis of laminated doubly-curved shell structures with arbitrary three-dimensional variations of the material orientation. Using a generalized higher-order kinematic model, the fundamental equations are derived in curvilinear principal coordinates, and they are numerically solved through the Generalized Differential Quadrature (GDQ) method. Then, a recovery procedure enables the reconstruction of the actual response of the three-dimensional solid. The accuracy of the method is demonstrated through different numerical examples that illustrate the effect of various material orientations on the mechanical response of straight and curved panels, thus offering a valuable tool for modelling complex structures.