We consider the scattering of time-harmonic electromagnetic plane waves by a piecewise homogeneous obstacle. In the interior of the obstacle there exists a core which may be a dielectric, a perfect conductor or an imperfect conductor. First, we obtain integral representations for the scattered fields incorporating all the boundary and transmission conditions. These representations are then used to derive the corresponding electric far field patterns. We prove reciprocity and scattering theorems and study the spectrum of the electric far field operator for these problems. Finally, we prove the optical theorem, that is a connection of the electric far field pattern to the scattering cross-section.