The demagnetization processes of antiferromagnetically exchange-coupled hard-soft-hard trilayer structures are studied based on the one-dimensional atomic chain model. It is found that when the magnetic anisotropy of soft layer is taken into account, the change of the soft layer thickness or the interfacial exchange coupling strength may lead to a transition from the reversible exchange-spring process to the irreversible process. For the trilayer structures with very thin soft layer, the demagnetization process exhibits typical reversible magnetic exchange-spring behavior. However as the thickness of soft layer increases, there appears a crossover point tc, after which the process becomes irreversible. There occurs also a critical interfacial exchange constant Ashc, above which the exchange-spring process is reversible. When AshAshc, the irreversible exchange-spring process is realized. The phase diagrams of reversible and irreversible exchange-spring process are mapped in the plane of the interfacial exchange coupling Ash and soft layer thickness Ns. The dependences of the bending field on the soft layer thickness for different interfacial exchange couplings are numerically examined.