We examine the use of ground penetrating radar (GPR) to simultaneously estimate snow and ice thickness. Since velocity is essential for depth inversion, we developed an automatic common mid-point (CMP) measurement system, which can work in an ultra-wide band. Envelope velocity spectrum, robust in reflection identification, is used to estimate the dielectric permittivity and layer thickness from CMP datasets. We tested our system on a 50-m-long test line on a brackish lagoon, i.e. Lake Saroma, in Hokkaido, Japan, in February 2012. Compared with the ground truth, the snow and ice thickness estimations possess a good accuracy, with a respective mean absolute error of about 2 cm (12%) and less than 2 cm (4%), which verifies the accuracy of their dielectric permittivity estimation. Then the estimated two-layer velocity model obtained by interpolation was used to continuously estimate the snow and ice thickness from the common-offset (CO) GPR profile acquired by a commercial GPR system. The mean absolute errors of snow and ice thickness estimated from the CO profile are respectively, about 3 cm (18%) and less than 6 cm (14%). Our system and method appear capable of accurately measuring the dielectric permittivity and thickness of other layered media.