In this study we incorporate the existing concept of fractional mobility into a stochastic framework for modeling the partial transport of mixed-size sediment. The model predicts the fractional transport rates with parameters such as the long-run moving probability, mean particle velocity, and fractional mobility, all varying with the dimensionless effective shear stress. Movement of bed load particles is treated as a random combination of single-step motions described by the pseudo four-state continuous-time Markov process whose long-run moving probability can be evaluated with the instantaneous entrainment probability and ratio of mean single-step holding time. A most updated version of entrainment probability taking into account both the rolling and lifting modes is adopted; the ratio of mean holding time is determined with a physically based relation derived experimentally. Two types of experiments are performed in this study: the colored bed experiments are carried out to observe the fractional mobility and partial transport; the plain bed experiments are conducted to observe the single-step bed load motions and mean particle velocity. The proposed model is widely tested with laboratory and field data pertaining to both partial and full transport conditions, and reasonably good agreement between the predicted and observed results is demonstrated. The model is then applied to evaluate the fractional mobility and explore the influence of sand content. The results reveal that the relation between fractional mobility and dimensionless effective shear stress is well approximated by the cumulative lognormal distribution, with its mean and standard deviation linearly decreasing with sand content for the range <0.34. The results imply that the existence of fine-grained sand in the gravel-sand mixture is favorable to the mobilization of sediment. At higher sand content the condition of partial transport exists within a narrower range of flows such that full transport is easier to achieve. The present study is the first to investigate the effect of sand content on the fractional mobility, thus providing new insights into the process of partial transport.