We present a detailed study on epitaxial bilayers made up of ferromagnetic (FM) Ni and antiferromagnetic (AFM) FexMn1−x layers on Cu(001). The AFM ordering temperature (TAFM) and the coupling at the interface of FM and AFM layer are deduced from polar magneto-optical Kerr effect measurements at different temperatures. The enhancement of coercivity for samples with different FexMn1−x layer thickness, Fe concentration, and FM-AFM interface roughness reveals that TAFM only depends on the layer thickness. The FM-AFM coupling strength is determined by the Fe concentration of the FexMn1−x layer and the interface roughness, but as the first two measurement series clearly show, these do not affect the ordering temperature, unlike earlier results for in-plane magnetization. We explain this difference by assuming that the spin structure of the AFM is distorted from the 3Q structure of the bulk material, in a way that depends on the magnetization direction of the adjacent FM layer. Additionally we discuss the dependence of FM-AFM coupling strength and AFM magnetic anisotropy on Fe concentration and interface roughness concluded from the thickness dependence of exchange-biased hysteresis loops.