Interface recombination in a complex multilayered thin-film solar structure causes a disparity between the internal open-circuit voltage (VOC,in), measured by photoluminescence, and the external open-circuit voltage (VOC,ex), that is, a VOC deficit. Aspirations to reach higher VOC,ex values require a comprehensive knowledge of the connection between VOC deficit and interface recombination. Here, a near-surface defect model is developed for copper indium di-selenide solar cells grown under Cu-excess conditions. These cell show the typical signatures of interface recombination: a strong disparity between VOC,in and VOC,ex, and extrapolation of the temperature dependent q·VOC,ex to a value below the bandgap energy. Yet, these cells do not suffer from reduced interface bandgap or from Fermi-level pinning. The model presented is based on experimental analysis of admittance and deep-level transient spectroscopy, which show the signature of an acceptor defect. Numerical simulations using the near-surface defects model show the signatures of interface recombination without the need for a reduced interface bandgap or Fermi-level pinning. These findings demonstrate that the VOC,in measurements alone can be inconclusive and might conceal the information on interface recombination pathways, establishing the need for complementary techniques like temperature dependent current–voltage measurements to identify the cause of interface recombination in the devices.