When two ferromagnetic thin films with different magnetic easy axes are coupled via the exchange interaction, the magnetization process becomes nontrivial. In this paper, we demonstrate that three-dimensional magnetization information in such a bilayer system can be accessed electrically by combining measurements of the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE). Specifically, we investigate a CoFe${}_2$O${}_4$(001)/Fe bilayer, where the insulating nature of CoFe${}_2$O${}_4$ ensures that these transport measurements selectively probe only the conductive Fe layer. By combining the AHE and ANE results and comparing them with a simple micromagnetic simulation, we probe the magnetic configuration of antiferromagnetically coupled Fe layer and suggest the emergence of a twisted magnetic structure near the interface.