<p>Inspired by the walking, jumping, and running of quadrupeds, a novel vibration isolation-absorption (BVIA) platform is proposed by applying a bistratal X-shaped structure and a multi-vertebra structure. Based on the mechanical-constitutive relationship, the static and dynamic models of the BVIA platform are established, and the force/stiffness-displacement curves are applied to reveal the loading capacity and quasi-zero stiffness characteristics. The vibration suppression performances of different parameters are investigated by amplitude-frequency curve and displacement transmissibility, and the results are verified by numerical methods. From the results, it can be found that the resonance peak significantly decreases due to the mutual promotion of vibration isolation and vibration absorption. The vibration suppression performance of the BVIA structure can be tuned flexibly by initial installation angle, rod length ratio, layer number, absorbed mass, stiffness coefficient, horizontal spring length, and excitation amplitudes. The proposed BVIA structure provides a useful reference for reducing the resonance peak and improving the vibration suppression performance in practical engineering applications.</p>