Composite structures are widely used in bridge and building construction. In fact, the majority of bridge structures, which are arguably the main subject of structural monitoring and damage identification, involve some form of composite components. The structural performance of a composite structure is dependent upon the conditions of the basic flexure-pertinent constituents, e.g., the material degradation (reduced Young's modulus) or cracking in the concrete slab of a slab-beam system, as well as the constituents that enable the composite effect, i.e., the shear connectors. It is therefore imperative that damages in a composite structure need be distinguished between "flexural" and "composite" nature. However, in the existing damage identification literature, especially when vibration-based techniques are employed, composite structures such as bridge decks are often treated as monolithic structures, and accordingly, structural parameters are identified in terms of gross flexural parameters without differentiating between flexure and shear link properties. This could lead not only to incorrect identification of the actual flexural properties but also potentially to misleading results in case serious damage to shear links occurs. In this paper, we will provide an overall discussion on the distinctive effects of flexural and shear link damages on the global structural stiffness in a composite beam. On this basis, the possibility and rationale to identify the mixed presence of flexural and shear link damage parameters using modal data from typical vibration tests are discussed. A genetic algorithm-based finite element model updating procedure is then implemented. The results show that separation of the flexural and shear link parameters is possible and satisfactory accuracy can be achieved with the FE model updating the proposed scheme.