To achieve coordinated optimization of vibration damping and electromagnetic shielding functions under complex vibration conditions, a multiphysics-coupled design approach is required. By adopting a composite configuration of viscoelastic damping materials and honeycomb shielding structures, the system can ensure an electromagnetic shielding effectiveness of over 40 dB while reducing the random vibration transmissibility to below 0.3. In engineering applications, frequency-segmented impedance matching technology is utilized to enable the honeycomb core to exhibit gradient impedance characteristics in the 200–2000 Hz range, thereby simultaneously achieving broadband vibration damping and electromagnetic wave absorption. In response to the spatial constraints typical of avionics equipment, a three-dimensional flexible conductive support system has been developed. This system maintains the integrity of the 0.5 μm vacuum coating on the cavity surface while employing a nonlinear stiffness design to suppress the peak resonance acceleration to within 5 g. Across the operational temperature range of -55°C to 125°C, the fluctuation in shielding effectiveness is controlled within ±1.2 dB.