In this study, an isogeometric finite element-boundary element (FE-BE) framework is proposed to investigate frequency-dependent hydrodynamic characteristics of elastic structures vibrating at free surface or in the vicinity of free surface. The overall numerical framework consists of two parts. In the first part, in vacuo dynamic characteristics are obtained by an isogeometric finite element method (IGAFEM) formulation. Then, in the second part, frequency-dependent generalized added mass and generalized hydrodynamic damping coefficients are obtained by an isogeometric boundary element method (IGABEM) formulation, assuming that the surrounding fluid is ideal, i.e., inviscid, incompressible and its motion is irrotational. To include free surface effects, the free surface boundary conditions are satisfied with an appropriate Green's function in the mathematical formulation. To show the applicability of the presented framework, an elastic cylindrical shell which was studied previously in the literature is investigated considering that the structure is partially or fully submerged into fluid of infinite depth. It is shown that the results obtained in this study compare very well with the results available in literature.