Interfacial behavior of associating species is important both from a fundamental physics perspective and from an industrial application point of view. Specifically, in the petroleum industry, self-association between asphaltene molecules causes them to aggregate and subsequently deposit on various surfaces, reducing the efficacy of oil extraction. The presence of surfactant-like molecules such as resins has been shown to inhibit asphaltene aggregation. A coarse-grained model capturing the structural and chemical features of asphaltene and resin would facilitate an understanding of physical principles behind the deposition behavior and guide mitigation strategies. To this end, we investigate the adsorption behavior of a mixture of nanoparticles and polymer chains onto an attractive surface through a classical density functional theory. Representing asphaltenes by nanoparticles and resins by polymer chains, we consider both nanoparticle-nanoparticle self-association and nanoparticle-polymer cross-association. We study the effect of the various chemical and physical characteristics of asphaltene and resin molecules such as association strengths, the chain length, the surface affinities and the nature of the surface on the adsorption amount of both nanoparticles and polymer molecules. We find that, due to the polymer stablizing effects, increasing nanoparticle-nanoparticle self-association strength enhances nanoparticle adsorption. Conversely, increasing nanoparticle-polymer interaction strength depresses nanoparticle adsorption. We also observe an inverse correlation between polymer chain length and nanoparticle adsorption. We rationalize the observed trends in light of interplay between different entropic and energetic driving forces operative in the system. Finally, we present an alternative framework where surface groups creating attraction are saturable and find that unlike adsorption onto an unsaturable surface, increasing nanoparticle-nanoparticle strength can inhibit nanoparticle adsorption.