To explore the effect of H addition (20 percent by volume) on stratified-premixed methane combustion in a turbulent flow, an experimental investigation on a new flame configuration of the Darmstadt stratified burner is conducted. Major species concentrations and temperature are measured with high spatial resolution by 1D Raman-Rayleigh scattering. A conditioning on local equivalence ratio (range from ϕ = 0.45 to ϕ = 1.25) and local stratification is applied to the large dataset and allows to analyze the impact of H addition on the flame structure. The local stratification level is determined as Δϕ/ΔT at the location of maximum CO mass fraction for each instantaneous flame realization. Due to the H addition, preferential diffusion of H is different than in pure methane flames. In addition to diffusing out of the reaction zone where it is formed, particularly in rich conditions, H also diffuses from the cold reactant mixture into the flame front. For rich conditions (ϕ = 1.05 to ϕ = 1.15) H mass fractions are significantly elevated within the intermediate temperature range compared to fully-premixed laminar flame simulations. This elevation is attributed to preferential transport of H into the rich flame front from adjacent even richer regions of the flow. Additionally, when the local stratification across the flame front is taken into account, it is revealed that the state-space relation of H is not only a function of the local stoichiometry but also the local stratification level. In these flames H is the only major species showing sensitivity of the state-space relation to an equivalence ratio gradient across the flame front.