We present a novel numerical method based on domain decomposition for the simulation of 3D geophysical marine controlled source electromagnetic (CSEM) measurements. Parts of the computational domain where it is reasonable to represent geoelectric properties in 2D, are discretized combining 2D mixed finite elements (FE) and Fourier expansion. The remaining part is discretized utilizing standard 3D FE methods. The method delivers high-accuracy simulations of marine CSEM problems with arbitrary 3D geometries while it considerably reduces the computational complexity of full 3D FE simulations for typical marine CSEM problems. For the particular scenarios considered in this work, the total CPU time required by the novel method is reduced approximately by a factor of five with respect to that needed by full 3D FE formulations.