We present a density functional theory (DFT) to describe adsorption in systems where molecules of associating fluids can bond (or associate) with discrete, localized functional groups attached to the surfaces, in addition to other fluid molecules. For such systems as water adsorbing on activated carbon, silica, clay minerals etc. this is a realistic model to account for surface heterogeneity rather than using a continuous smeared surface-fluid potential employed in most of the theoretical works on adsorption on heterogeneous surfaces. Association is modelled within the framework of first order thermodynamic perturbation theory (TPT1). The new theory accurately predicts the distribution of bonded and non-bonded species and adsorption behavior under various conditions of bulk pressure, surface-fluid and fluid-fluid association strengths. Competition between the surface-fluid and fluid-fluid association is analyzed for fluids with multiple association sites and its impact on adsorption is discussed. The theory, supported by simulations demonstrates that the extent and the nature of adsorption (e.g. monolayer) vary with the number of association sites on the fluid molecules.