Model systems of organic self-assembled monolayers are important in achieving full atomic-scale understanding of molecular-electronic interfaces as well as the details of their charge transfer physics. Here we use two-photon photoemission to measure the evolving unoccupied and occupied interfacial electronic structure of two thiolate species, thiophenol and p-fluorothiophenol, adsorbed on Cu(111) as a function of molecular coverage. Our measurements focus on the role of adsorbates in shifting surface polarization and effecting surface electron confinement. As the coverage of each molecule increases, their photoemission-measured work functions exhibit nearly identical behavior up to 0.4-0.5 ML, at which point their behavior diverges; this behavior can be fit to an interfacial bond model for the surface dipole. In addition, our results show the emergence of an interfacial electronic state 0.1-0.2 eV below the Fermi level. This electronic state is attributed to quantum-mechanical-confinement shifting of the Cu(111) surface state by the molecular adsorbates.