Finite rate chemistry is investigated in turbulent N2-diluted H2 diffusion flames by means of laser spectroscopic methods and a numerical model of combustion. The major species occurring in these hydrogen flames or the temperature are measured with SRS (Spontaneous Raman Spectroscopy) or Rayleigh spectroscopy. Some minor species, the radical OH and the pollutant NO, are simultaneously measured with linear LIF (Laser Induced Fluorescence). Multidimensional pdfs (probability density function) can be deduced from these measurements. Use is made of a numerical model with two principal variables, mixture fraction ξ and reaction progress variable η, as a basis for discussion of the experimental results. A κ-ε-turbulence model together with a two-dimensional presumed pdf for the coupling of turbulence and chemistry are applied. So, experimental two-dimensional pdfs as well as mean values of ξ and η as functions of the position in the flame are deduced from the simultaneous measurements. The experimental and theoretical spatial maxima of the mean OH molefraction agree well in magnitude, despite the correlation coefficient between ξ and η of the measured pdf can be as high as 0.5. The neglect of this covariance for the calculation of the presumed pdf is quantified. It results in clear deviations for the OH molefraction. The experimental NO and OH molefractions are better simulated by flame calculations carried out with the presented combustion model than by the also shown calculations based on a single variable for description of chemistry.