Monitoring the snow water equivalent (SWE) is critical to effective management of water resources in many parts of the world that depend on the mountain snowpack for water storage. There are currently no methods to remotely sense SWE with accuracy over large lateral distances in the steep and often forested terrain of mountain basins. Previous studies have shown that measurements of ground-penetrating radar (GPR) velocity can provide accurate estimates of SWE in dry snow. Introduction of liquid water into the snowpack results in a three-phase system that cannot be accurately characterized with GPR velocity alone. We show that measuring the frequency-dependent GPR signal attenuation and velocity provides a direct estimate of the complex dielectric permittivity. Because the imaginary component is a function only of liquid water content, we can utilize both the real and imaginary components of the permittivity to estimate liquid water content, snow density, and SWE using existing empirical relationships that are valid in the pendular regime. We tested this new method at two field sites and found that the estimates were accurate to within 12% of gravimetric methods in both a moist and a dry snowpack. GPR has the potential to provide SWE estimates across large lateral distances over a broad range of snow conditions.