Heat transfer in the interstitial materials of vacuum insulation panel (VIP) occurs by conduction through the solid structure and radiation through the pore. This process is analyzed with the discrete ordinates interpolation method (DOIM) incorporated with the commercial code Fluent. This combined analysis is shown to yield an accurate reference solution. The interstitial material of VIP is modeled as a 1-D plane parallel medium with constant properties and the walls are assumed to be isothermal and diffuse. It is found that the effect of wall emissivity is reduced for a non-scattering medium. The effective thermal conductivity is significantly larger than that predicted by simple additive approximation for low emissivity boundaries in an intermediate optical thickness range. In contrast, simple additive approximation using Rosseland approximation for the radiative conductivity predicts well for optically thick medium with high emissivity boundaries. Additive solution also matches with the combined analysis for optically thin medium, but the effect of wall emissivity is more dominant in the other cases. When the contact resistance between the wall and the filler material is added to the analysis, the effect of conduction-radiation interaction near the wall is compensated with the contact resistance. Therefore the wall emissivity is more influential than expected and the effective thermal conductivity can be reduced. The effect of various scattering modes has also been investigated. It is found that backward scattering medium is more effective in reducing total heat transfer while isotropic scattering medium is almost identical with non-scattering medium. Thus combined analysis with the modeling of contact resistance is expected to be used in the optimization of insulation performance of VIP with artificial core structure and radiation shields.