We develop a new formulation of the integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) field computation in large-scale models with multiple inhomogeneous domains. This problem arises in many practical applications including modeling the EM fields within the complex geoelectrical structures in geophysical exploration. In geophysical applications, it is difficult to describe an earth structure using the horizontally layered background conductivity model, which is required for the efficient implementation of the conventional IE approach. As a result, a large domain of interest with anomalous conductivity distribution needs to be discretized, which complicates the computations. The new method allows us to consider multiple inhomogeneous domains, where the conductivity distribution is different from that of the background, and to use independent discretizations for different domains. This reduces dramatically the computational resources required for large-scale modeling. In addition, using this method, we can analyze the response of each domain separately without an inappropriate use of the superposition principle for the EM field calculations. The method was carefully tested for the modeling the marine controlled-source electromagnetic (MCSEM) fields for complex geoelectric structures with multiple inhomogeneous domains, such as a seafloor with the rough bathymetry, salt domes, and reservoirs. We have also used this technique to investigate the return induction effects from regional geoelectrical structures, e.g., seafloor bathymetry and salt domes, which can distort the EM response from the geophysical exploration target.