  Pulsar dispersion measures (DMs) have been used to model the electron density
of the interstellar medium (ISM) in the Galactic disk as a plane-parallel
medium, despite significant scatter in the DM-distance distribution and strong
evidence for inhomogeneities in the ISM. We use a sample of pulsars with
independent distance measurements to evaluate a model of the local ISM in the
thick disk of the Galaxy that incorporates turbulent fluctuations, clumps, and
voids in the electron density. The latter two components are required because
$\sim 1/3$ of the lines of sight are discrepant from a strictly plane parallel
model. A likelihood analysis for smooth components of the model yields a scale
height $z_0=1.57^{+0.15}_{-0.14}$ kpc and a mid-plane density $n_0=0.015 \pm
0.001$ cm$^{-3}$. The scatter in the DM-distance distribution is dominated by
clumps and voids but receives significant contributions from a broad spectrum
of density fluctuations, such as a Kolmogorov spectrum. The model is used to
identify lines of sight with outlier values of DM. Three of these pulsars,
J1614$-$2230, J1623$-$0908, and J1643$-$1224, lie behind known HII regions, and
the electron density model is combined with H$\alpha$ intensity data to
constrain the filling factors and other substructure properties of the HII
regions (Sh 2-7 and Sh 2-27). Several pulsars also exhibit enhanced DM
fluctuations that are likely caused by their lines of sight intersecting the
superbubble GSH 238+00+09.
