We present a new formalism to describe the ratios and profiles of emission lines from hydrogen in Balmer-dominated shocks. We use this model to interpret the measured widths and ratios of broad and narrow Hα, Hβ, and Lyα emission lines in supernova remnants (SNRs). Our model results agree fairly well with those obtained previously by Chevalier, Kirshner, & Raymond and are consistent with observations of several SNRs. The same model fails to account for the ratio of broad to narrow line emission from the reverse shock in SNR 1987A as observed by Heng and coworkers. We suggest that this discrepancy between theory and observation results from a faulty assumption that Balmer-dominated shocks can be treated as sharp discontinuities. If the spatial structure of the shock transition zone is taken into account, the predicted ratios of broad to narrow line emission in most SNRs will change by modest factors, but the ratio in SNR 1987A will increase substantially. Significantly greater shock velocities will be required to account for the observed full widths at half-maximum of the broad emission lines in most SNRs.