This paper presents a method for joint retrieval of the ocean surface wind and current vectors using the backscatter and the Doppler frequency shift measured by spaceborne single-beam single-polarization synthetic aperture radar (SAR). The retrieval method is based on the Bayesian approach with the a priori information provided by atmospheric and oceanic models for surface wind and currents, respectively. The backscatter and Doppler frequency shift are estimated from the along-track interferometric SAR system TanDEM-X data. The retrieval results are compared against in-situ measurements along the Swedish west coast. It is found that the wind retrieval reduces the atmospheric model bias compared to in-situ measurements by about 1 m/s for wind speed, while the bias reduction in the wind direction is minor as the wind direction provided by the model was accurate in the studied cases. The ocean model bias compared to in-situ measurements is reduced by about 0.04 m/s and 12 circle for current speed and direction, respectively. It is shown that blending SAR data with model data is particularly useful in complex situations such as atmospheric and oceanic fronts. This is demonstrated through two case studies in the Skagerrak Sea along the Swedish west coast. It is shown that the retrieval successfully introduces small scale circulation features detected by SAR that are unresolved by the models and preserves the large scale circulation imposed by the models.