We present data on the photoabsorption spectrum of lithium atoms in an electric field at energies between the saddle point of the Stark potential and below the field-free ionization threshold. The spectrum displays a sequence of sharp resonances and a sequence of broad ones. We find that the broad resonances arise from the classically forbidden reflection of waves above a dynamical potential barrier. The recurrence spectrum is also observed and it is dramatically affected by above-barrier reflections. We have developed a semiclassical theory that interprets the spectra using quasiclassical trajectories that undergo above-barrier reflection.