We examine the structure of the post-shock region in supernova remnants (SNRs). The ``shock transition zone'' is set up by charge transfer and ionization events between atoms and ions, and has a width $\sim 10^{15}$ cm$^{-2}$ $n^{-1}_0$, where $n_0$ is the total pre-shock density (including both atoms and ions). For Balmer-dominated SNRs with shock velocity $v_s \gtrsim 1000$ km s$^{-1}$, the Rankine-Hugoniot conditions for ion velocity and temperature are obeyed instantly, leaving the full width at half-maximum (FWHM) of the broad H$α$ line versus $v_s$ relation intact. However, the spatial variation in the post-shock densities is relevant to the problem of Ly$α$ resonant scattering in young, core-collapse SNRs. Both two- (pre-shock atoms and ions) and three-component (pre-shock atoms, broad neutrals and ions) models are considered. We compute the spatial emissivities of the broad ($ξ_b$) and narrow ($ξ_n$) H$α$ lines; a calculation of these emissivities in SN 1006 is in general agreement with the computed ones of Raymond et al. (2007). The (dimensionless) spatial shift, $Θ_{\rm{shift}}$, between the centroids of $ξ_b$ and $ξ_n$ is unique for a given shock velocity and $f_{\rm{ion}}$, the pre-shock ion fraction. Measurements of $Θ_{\rm{shift}}$ can be used to constrain $n_0$.

25 pages, 8 figures. Accepted by Astrophysical Journal