Soft robotics requires structural systems capable of performing complex and programmable deformations to adapt to unstructured or dynamic environments. Shape memory materials (SMMs) offer a promising solution owing to their shape memory effect and stimulus-responsive adaptability. However, actuators relying on a single type of SMM are often constrained by nonlinear actuation behavior and limited stiffness variation, which restrict their ability to achieve coordinated, multifunctional responses. Addressing these challenges, this study introduces a hybrid programmable morphing structure that integrates a shape memory polymer (SMP) and a shape memory alloy (SMA) to realize cooperative actuation and adaptive stiffness variation within a single unit. In the proposed configuration, the SMA springs act as thermally activated actuators that generate deformation. The SMP cylindrical core employs its shape memory effect to realize reversible shape locking and serves as a thermal switch that enables controlled stiffness variation through temperature regulation. A coupled numerical model was established to describe the cooperative behavior between the SMA and SMP components, and the numerical results were validated through experimental testing. The agreement between simulations and experiments confirms the feasibility and repeatability of the proposed design. The structure achieves a maximum bending angle of 55° under dual-SMA actuation and 42° under single-SMA actuation, while maintaining any intermediate shape during thermal cycling. Furthermore, the hybrid system demonstrates a reversible six-fold increase in stiffness and a motion range extending up to three times its original length, representing a significant improvement over conventional single-material soft actuator. Moreover, the proposed hybrid structure offers a flexible strategy for programmable morphing and demonstrates scalable applicability in practical applications, such as adaptive grasping, reconfigurable locomotion, and environmental exploration. In conclusion, this work provides a feasible and generalizable framework for integrating multiple SMM into programmable morphing structures which can be applied into multifunctional soft robotic systems.