The in-plane auxetic honeycomb sandwich panels (AHSPs) with polyurea-metal laminate (PML) as faceplates were proposed, and their vibration and acoustic properties were investigated. The natural frequency, damping loss factor, sound transmission loss (STL), and sound field pressure distribution were simulated by the finite element, which was then compared with the AHSP without a polyurea layer. The sound insulation properties of the AHSPs with PML faceplates were significantly enhanced due to the viscoelastic energy consumption of the polyurea layer. By changing the thickness of the polyurea layer and adopting different honeycomb geometries, the sound insulation ability of the sandwich plate could be further enhanced. The average STL rose by 2.3–4.7 dB when the polyurea layer thickness was increased, hence significantly improving the noise suppression ability of the AHSPs. When the geometric tilt angle θ of the honeycomb core is −45°, the sandwich panel exhibits superior sound insulation performance.