We propose an interface-proximity model that allows us to solve a longstanding puzzle regarding large discrepancies between the experimentally observed and theoretically estimated values of exchange-bias field Heb in coupled ferromagneticantiferromagnetic (FAF) metallic films. In this proposed model, switchable uncompensated (UC) AF spins in contact with an F layer are taken into account as an additionally inserting layer that is chemically or magnetically distinguishable from each of the nominal AF and F layers. Reductions in Heb, enhancements in coercivity, and other exchange-bias behaviors typically observed in experiments are very well reproduced from this model. The switchable interfacial UC region with a sizable thickness, heretofore ignored, plays a crucial role in the exchange bias phenomenon.