To address the limited wave domain signal processing capabilities of traditional single-polarized stacked intelligent metasurfaces (SIMs) in holographic multiple-input multiple-output (HMIMO) systems, which stems from limited integration space, this paper proposes a dual-polarized SIM (DPSIM) architecture. By stacking dual-polarized reconfigurable intelligent surfaces (DPRIS), DPSIM can independently process signals of two orthogonal polarizations in the wave domain, thereby effectively suppressing polarization cross-interference (PCI) and inter-stream interference (ISI). We introduce a layer-by-layer gradient descent with water-filling (LGD-WF) algorithm to enhance end-to-end performance. Simulation results show that, under the same number of metasurface layers and unit size, the DPSIM-aided HMIMO system can support more simultaneous data streams for ISI-free parallel transmission compared to traditional SIM-aided systems. Furthermore, under different polarization imperfection conditions, both the spectral efficiency (SE) and energy efficiency (EE) of the DPSIM-aided HMIMO system are significantly improved, approaching the theoretical upper bound.