Recent studies have shown that preferential adsorption of random heteropolymers on disordered multifunctional surfaces occurs when the statistics describing the monomer sequence and the statistics describing the distribution of sites on the surface are matched in a certain way. The polymers undergo a sharp transition from weak to strong adsorption, indicative of pattern recognition. In this work, we continue to study the behavior of random heteropolymers as they adsorb on disordered surfaces using a nonreplica mean-field model that accounts for distinct and competitive interactions both among the polymer segments as well as between the polymer segments and sites on the surface. We find that strong interactions between polymer segments and between segments and sites on the surface are dominated by energetically favorable contacts among the segments and between segments and surface sites, respectively. Our results indicate that the polymers strongly adsorb in conformations that allow for a very small number of contacts between the segments, implying that the polymers strongly adsorb in relatively flat and stretched conformations.