The problem of acoustic source depth discrimination was introduced as a way to get basic information on source depth in configurations where accurate depth estimation is not feasible. It is a binary classification problem, aiming to evaluate whether the source is near the surface or submerged. Herein, the classification relies on a signal measured with a horizontal line array in shallow water. Knowing the source-array distance is not required but the source bearing has to be close to the array endfire. Signal processing relies on a normal-mode propagation model, and thus requires prior knowledge of the mode characteristics. The decision relies on an estimation of the trapped energy ratio in mode space. The performance is predicted with simulations and Monte Carlo methods, allowing one to compare several estimators based on different mode filters, and to choose an appropriate decision threshold. The impact on performance of frequency, noise level, horizontal aperture, and environmental mismatch is numerically studied. Finally, the approach is validated on experimental data acquired with a horizontal line array deployed off the coast of New Jersey, and the impact of errors in the environmental model is illustrated. The investigated approach successfully identifies a surface ship and a submerged towed source.