Magnetic hysteresis properties of antiferromagnetically exchange-coupled bilayer structures, in which the two magnetic layers have different magnetic parameters and thicknesses, are studied within the framework of the Stoner--Wohlfarth model. Analytical expressions for the switching fields corresponding to the linear magnetic states are obtained. By adjusting the magnetic parameters or thicknesses of layers, nine different types of easy-axis hysteresis loops may exist. The phase diagram of easy-axis hysteresis loops is mapped in the k₁ and k₂ plane, where k₁ and k₂ are the ratios of magnetic anisotropy to the interlayer exchange coupling of the two magnetic layers, respectively.