The accurate calculation of intermolecular interaction energies with density functional theory requires methods that include a treatment of long-range, nonlocal dispersion correlation. In this work, we explore the ability of the exchange-hole dipole moment (XDM) dispersion correction to model molecular surface adsorption. Adsorption energies are calculated for six small aromatic molecules (benzene, furan, pyridine, thiophene, thiophenol, and benzenediamine) and the four DNA nucleobases (adenine, thymine, guanine, and cytosine) on the (111) surfaces of the three coinage metals (copper, silver, and gold). For benzene, where the experimental reference data is most precise, the mean absolute error in the computed absorption energies is 0.04 eV. For the other aromatic molecules, the computed binding energies are found to be within 0.09 eV of the available reference data, on average, which is well below the expected experimental uncertainties for temperature-programmed desorption measurements. Unlike other dispersion-corrected functionals, adequate performance does not require changes to the canonical XDM implementation, and the good performance of XDM is explained in terms of the behavior of the exchange hole. Additionally, the base functional employed (B86bPBE) is also optimal for molecular studies, making B86bPBE-XDM an excellent candidate for studying chemistry on material surfaces. Finally, the noncovalent interaction (NCI) plot technique is shown to detect adsorption effects in real space on the order of tenths of an eV.