Beam propagation and reflection are studied at the interface between a Kerr medium and a saturable absorbing nonlinear medium. For spatial solitons propagating nearly tangent to the interface, slowly varying envelope theory describes beam behavior. Phenomena are studied using numerical beam propagation and dynamical systems arguments. Projecting the dynamics onto the soliton modes of the nonabsorbing medium, an effective-particle theory is developed for the reflected beam. The results of the effective-particle theory and the numerical analysis are compared, and a heuristic criterion for predicting reflection and absorption of beams is derived.