In state-of-the-art, anode-supported, solid oxide fuel cells (SOFC) the fuel electrode is made of two different porous Ni/stabilized zirconia layers, both with specified phase compositions and microstructural characteristics. It is generally assumed that electro-oxidation of fuel takes place in the thinner anode functional layer (AFL) adjacent to the electrolyte, while gas diffusion takes place in the thicker anode substrate (AS). This assumption is not always applicable and established models fail. This paper introduces a generally valid equivalent circuit model by means of a three-channel transmission line model (3CTLM) that considers electro-oxidation, ionic conduction and gas diffusion. It is parameterized by (i) impedance measurements on model-electrodes, (ii) conductivity measurements, (iii) FIB/SEM-tomography and (iv) gas theory. The complex impedance curve is derived by a newly developed numerical routine that uses calculation steps from network analysis. A model validation is performed by comparing measured and simulated impedance spectra of anode-supported SOFCs varying in AFL thickness from 3 to 22 mu m. The 3CTLM is capable of predicting the impedance of any Ni/stabilized zirconia anode design. A model-based optimization is demonstrated, selecting different ionic conducting phases in AFL and AS for combinations of Ni/10Sc1CeSZ, Ni/8YSZ and Ni/3YSZ, across a temperature range of 600-900 degrees C.