A new hybrid formalism in the frequency domain is presented, based on a combination of the boundary integral equation (BIE) technique, the finite element (FE) method and the finite difference time domain (FDTD) algorithm. An FE method and FDTD are used to describe the inhomogeneous parts of the simulation domain, whereas large homogeneous portions of the simulation space are modeled with a BIE. To solve the global matrix system efficiently, a biconjugate gradient solver is used. To calculate the matrix-vector products in each iteration step of the solution process, the system matrix is required for the FE and the BIE subregions. For FDTD subregions, we will either construct a system matrix or we will calculate matrix-vector products directly relying on FDTD. Guidelines will be given to choose the most efficient approach for each FDTD subdomain. To illustrate the efficiency of the new method and to compare the new approach with other (hybrid) methods, three representative configurations are studied.