Spectral elements are preferred for accurate prediction of transitional flows, whereas finite elements are better suited for, possibly non-smooth, deforming solid objects. A new overlapping domain technique is proposed that couples spectral and finite elements. This technique aims to capture efficiently the pressure jump and deformation rates of thin solids moving in a fluid. The solid object is fully embedded in a finite element fluid mesh and the coupling interface is situated in the fluid domain. The technique is particularly suited for simulation of cardiovascular fluid-structure interaction problems, such as flow through heart valves. In this paper the overlapping domain technique will be explained and several numerical benchmarks will be presented to test the fluid-fluid coupling between spectral and finite elements. The results obtained demonstrate that the technique is accurate and stable.