Electrochemical impedance spectroscopy (EIS) is a very powerful tool for the diagnosis and characterisation of fuell cells (FC). However, there is still a lack of physico-chemically consistent models that include parameters with a clear physical meaning and can be related to intrinsic parameters of FC. To fill this knowledge gap, this paper presents a novel, mechanistically-based and computationally-efficient FC modeling framework for time and frequency domain simulations. Furthermore, the model consistently handles forward and backward reactions, ensuring its validity at all current densities. These features enable the development of a hybrid methodology for parameterising the FC model in both domains, resulting in unprecedented accuracy in determining the internal states around which the EIS perturbation is applied. Furthermore, innovative modeling framework incorporates a 1D analytical solution of FC impedance that for the first time accounts for both electrodes, the membrane and individual effects of the electrodes coupled to the respective GDL and channel, all significantly impacting the accuracy of the model. This was confirmed by state-of-the-art reproduction of experimental data with R$^2$ values exceeding 0.965 for data not used in the parameterisation. The presented modeling framework thus provides a modelling basis for observer functionalities beyond the state-of-the-art.