A simple microscopic model is used to study the effect played by interface roughness on the intriguing thermal-history-dependent properties observed in exchange-coupled antiferromagnetic (AF)/ferromagnetic (FM) bilayers. The model assumes two monolayers, one with AF-coupled compensated spins and the other with FM-coupled spins, with a fraction of them randomly substituted by spins from the AF layer to represent the interface roughness. The equations for the local magnetizations are set up in a mean-field approximation with Ising interactions and solved numerically for arbitrary temperature. Following the experimental procedure, upon cooling the system in an applied field, the model exhibits an intrinsic unidirectional anisotropy and coercitivity which are dependent on the field-temperature history. The dependence of the exchange bias field (He) and coercitive field (Hc) on the cooling field, initial and final temperatures, and interlayer exchange interaction are qualitatively similar to experimental observations. The results represent a definitive indication that the random field arising from interface roughness is responsible for the irreversibility and metastability properties of AF/FM bilayers.