This paper describes a set of improved C0-compatible composite shell finite elements for evaluating the global dynamic response (natural frequencies and mode shapes) of sandwich structures. Combining a through-the-thickness displacement approximation of variable high order with a first-order zigzag function, the proposed finite elements are suited for modelling sandwich plates and doubly curved shells with a non-uniform thickness and are more accurate than conventional models based on the first- and third-order shear deformation theories, especially in sandwich panels with highly heterogeneous properties. The new finite element model is then validated by a comparison with the standard shell and 3D solid models. From these investigations, it can be concluded that adding a zigzag function even to high-order polynomial approximations of the through-the-thickness displacement is a useful tool for refining the modelling of sandwich structures. In addition, the proposed formulation is sufficiently versatile to represent with the same level of accuracy the behaviour of thin-to-thick laminated shells as well as of strongly heterogeneous sandwich structures.