This paper presents a Reynolds averaged Navier Stokes turbulent combustion model for CH4/H2/air mixtures which includes the effect of heat losses and flame stretch. This approach extends a previous model concept designed for methane/air mixtures and improves the prediction of flame stabilization when hydrogen is added to the fuel. Heat loss and stretch effects are modeled by tabulating the consumption speed of laminar counterflow flames in a fresh-to-burnt configuration with detailed chemistry at various heat loss and flame stretch values. These computed values are then introduced in the turbulent combustion model by means of a turbulent flame speed expression which is derived as a function of flame stretch, heat loss, and H2 addition. The model proposed in this paper is compared to existing models on experimental data of spherical expanding turbulent flame speeds. The performance of the model is further validated by comparing computational fluid dynamics predictions to experimental data of an atmospheric turbulent premixed bluff-body-stabilized flame fed with CH4/H2/air mixtures ranging from pure methane to pure hydrogen.