We study the energy spectrum of atoms trapped in a vertical one-dimensional optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our model includes the long-range Casimir-Polder potential together with a short-range Lennard-Jones potential, which are considered nonperturbatively with respect to the optical lattice potential. We find an intricate energy spectrum which contains a pair of loosely bound states localized close to the surface in addition to a surface-modified Wannier-Stark ladder at long distances. Atomic interferometry involving those loosely bound atom-surface states is proposed to probe the adsorption dynamics of atoms on mirrors.