The article presents the results of a systematic study of the crystalline structure, microstructure, and hysteresis properties of (Cr80Mn20)/Fe bilayers, deposited on buffer coatings of various metals (Cr, Fe, W, Ta). It has been established that depending on the composition of the buffer coating and the thickness of the Cr-Mn layer, the latter develops body-centered cubic structure with either the (110) or (200) texture, or none. It is shown that the Cr-Mn layer is a source of increased coercivity in the adjacent Fe layer and when is in a certain structural state and has a relatively large thickness (100 nm) induces exchange bias in the Fe layer. The regularities obtained are interpreted in terms of the antiferromagnetic ordering of Cr-Mn and its relatively weak magnetic anisotropy