Source localization from external data such EEG or MEG, requires a good understanding of the electromagnetic behavior of the patient head. Several models can been used, representing more or less complex geometrical shapes, and conductivity profiles. Different numerical methods allow to cope with different types of models: the Finite Element Method (FEM) can handle very general conductivity models, whereas the Boundary Element Method (BEM) is limited to piecewise constant conductivity. On the other hand, it is easier with BEM than with FEM to accurately represent sources in isotropic media. Thanks to domain decomposition, we propose to independently use BEM or FEM in different sub-domains. In the EEG forward problem considered, the BEM is limited to the domain containing sources (the brain) while the other tissues are handled with the FEM. This leads to an accurate description of the sources while allowing for inhomogeneous and anisotropic conductivity. The coupled method is first validated against analytical solutions in multi-sphere models. Results of the forward problem are presented for a four-layer realistic head-model incorporating a burr-hole in the skull. Convergence of the iterative coupling algorithm is analyzed numerically, and the results are compared to the BEM alone, and the FEM alone. For the BEM we use the symmetric BEM of OpenMEEG, and for the FEM we use a tetraedric FEM, with or without the dipole subtraction method. The domain decomposition framework provides a way of taking the best advantage of both methods, thus significantly improving the accuracy in the resolution of the forward EEG problem, as well as time and memory consumption. As a byproduct of this research, domain decomposition can also be used for BEM or FEM by themselves, in order to break down a large problem into several smaller sub-problems. This can have interesting consequences for acceleration, at the expense of a slight memory overhead.