Composite elements are widely used in engineering disciplines such as mechanical, aerospace and civil engineering. For composite elements, where the different layers are not rigidly connected, full layer interaction cannot be achieved and therefore classical theories for stress and displacement analysis are no longer applicable. Higher-order theories for composite beams that consider interlayer slips as additional degrees of freedom have been developed, for example, in [1], [2]. These and many other references have in common that the governing (coupled) differential equations are either solved analytically or by a Ritz-based approach. However, these solutions are very difficult or virtually impossible to obtain for arbitrary boundary conditions, cross sections and load cases, and even more for two-dimensional cases (e.g. plates). Therefore, computationally expensive simulations using continuum and cohesive elements are needed to accurately predict the behavior of arbitrary composite elements with interlayer slip. To bridge the gap between the higher-order theories and time-consuming numerical simulations, novel beam elements for weakly bonded composites will be presented and solved using isogeometric and finite element analyses. The efficiency and accuracy of the elements, as well as the overall superior accuracy of the isogeometric formulation, are demonstrated using different benchmark problems. The global error is evaluated by computing discrete eigenvalue spectra and errors in eigenmodes. Additionally, novel closed-form descriptions of these eigenfrequency spectra will be presented by extending the derivations in, for example [3], [4], in order to find exact solutions to the typical discrete coupled interior equations of motion. These analytical spectra are derived for B-Splines of varying continuity, as well as for Lagrangian and Hermitian basis functions. Finally, potential future applications of the developed methods are discussed, such as dispersion optimized elements using blended quadrature rules, and extensions to composite plates with interlayer slip.