In studying the mass balance of polar ice sheets, fluctuations in firn density near the surface is a major uncertainty. In this paper, we explore these variations at locations on the Greenland Ice Sheet and at the Dome C location in Antarctica. Borehole in situ measurements, snow radar echoes, microwave brightness temperatures, and modeling results from the Community Firn Model (CFM) are used. It is shown that firn density profiles can be represented using three processes: "long-scale"and "short-scale"density variations and "refrozen layers". Consistency with this description is observed in the dynamic range of airborne 0.5-2GHz brightness temperatures and snow radar echo peaks in measurements performed in Greenland in 2017. Based on these insights, a new analytical partially coherent model is implemented to explain the microwave brightness temperatures using the three-scale description of the firn. Short- and long-scale firn processes are modeled as a 3D continuous random medium with finite vertical and horizontal correlation lengths as opposed to past 1D randomly layered medium descriptions. Refrozen layers are described as deterministic sheets with planar interfaces, with the number of refrozen-layer interfaces determined by radar observations. Firn density and correlation length parameters used in forward modeling to match measured 0.5-2GHz brightness temperatures in Greenland show consistency with similar parameters in CFM predictions. Model predictions also are in good agreement with multi-angle 1.4GHz vertically and horizontally polarized brightness temperature measured by the Soil Moisture and Ocean Salinity (SMOS) satellite at Dome C, Antarctica. This work shows that co-located active and passive microwave measurements can be used to infer polar firn properties that can be compared with predictions of the CFM. In particular, 0.5-2GHz brightness temperature measurements are shown to be sensitive to long-scale firn density fluctuations with density standard deviations in the range of 0.01-0.06gcm-3 and vertical correlation lengths of 6-20cm.