In some Earth materials, significant induced polarization (IP) phenomena are occurring when an electric perturbation is applied. These mechanisms are described by a frequency-dependent complex resistivity (CR). The study of the CR spectral signature allows to access indirectly to several properties of interest of the subsurface linked to the interaction between the pore space and fluids. CR is usually studied using the electrical method with a direct current approximation, neglecting by the way electromagnetic (EM) induction that can occur in the data. However, EM induction increases with frequency and offset, resulting in limitations at high frequencies or for the investigation of deep target. We implemented a frequency-dependent CR in a 3-D finite-differences (FD) modelling and inversion code for frequency domain controlled-source electromagnetic (CSEM) data to take into consideration IP information contained in EM data or reciprocally. The CSEM methods are resistivity imaging techniques using multifrequency EM fields that fully take into account EM induction with large investigation depth. Following a preliminary sensitivity study, a multistage inversion framework was designed to constrain the multiparameter inverse problem. Furthermore, to manage the increasing number of parameters, a second-order polynomial parametrization is used to describe independently frequency variation of CR norm and phase. We demonstrate the method through 1-D and 3-D synthetic data inversions for a deep-target model. We show that we were able to recover the CR and its frequency variation from CSEM data in the IP/EM coupling domain for 1-D targets. The problem of deep polarizable 3-D targets is more challenging and the resolution of the recovered CR spectrum was impacted. Nevertheless, we retrieved from a model containing several polarizable anomalies some crucial information allowing the discrimination of the targets from the non-polarizable background and from different spectral CR signatures. Our inversion strategy allows thus accessing to IP parameters of the medium in an extended frequency domain by fully taking EM induction information into account.