We investigated the exchange bias fields at the NiFe/FeMn and FeMn/CoFe interfaces in 18.9-nm NiFe/15.0-nm FeMn/17.6-nm CoFe trilayer thin films as the annealing temperature was varied from room temperature to $250^{circ}C$ in a vacuum for 1 hour in a magnetic field of 150 Oe. Interestingly, magnetic hysteresis (M-H) measurements showed that NiFe/FeMn/CoFe trilayer thin films exhibited a completely contrasting variation of the exchange bias fields at both the NiFe/FeMn and FeMn/CoFe interfaces with annealing temperatures. High-angle X-ray diffraction (XRD) measurements indicated the absence of any discernible effect of thermal treatment on the NiFe(111) and FeMn(111) peaks. The compositional depth profile obtained from X-ray photoelectron spectroscopy (XPS) results presented the asymmetric compositional depth profiles of the Mn and Fe atoms throughout the FeMn layer. We contend that this asymmetric compositional depth profile and the preferential Mn diffusion into the NiFe layer, compared to that into the CoFe layer, are conclusive experimental evidence of the contrasting variation of the exchange bias fields at two interfaces having a common polycrystalline FeMn(111) layer.