Passive vibration isolation has the advantages of simple structure, high reliability, and strong ability to absorb high-frequency vibration. Active vibration isolation has wide application range, strong controllability, and good vibration suppression effect for specific frequency band. Active and passive integrated vibration isolation technology combines the characteristics of both and has obvious advantages in dealing with the complex vibration environment in modern engineering practice. In this work, piezoelectric stack actuator is selected as the active control output source and vulcanized butyl rubber is used as the passive vibration absorber. The dynamic model of the novel active and passive integrated isolator is established, then the effects of different parameters on its vibration transmission performance are studied. Furthermore, a typical two-degree-of-freedom vibration isolation system model is established. By comparing the change of vibration transmissibility under different feedback forms, the design of the feedforward–feedback composite controller is applied. Finally, a double-layer vibration isolation test platform is built to verify the vibration reduction capability of the active and passive integrated isolator. The experimental results show that both the passive vibration absorption and active vibration suppression functions of this novel vibration isolator are particularly effective.