  We present a comparative study of molecular and ionized gas kinematics in
nearby galaxies. These results are based on observations from the EDGE survey,
which measured spatially resolved $^{12}$CO(J=1-0) in 126 nearby galaxies.
Every galaxy in EDGE has corresponding resolved ionized gas measurements from
CALIFA. Using a sub-sample of 17 rotation dominated, star-forming galaxies
where precise molecular gas rotation curves could be extracted, we derive CO
and H$\alpha$ rotation curves using the same geometric parameters out to
$\gtrsim$1 $R_e$. We find that $\sim$75% of our sample galaxies have smaller
ionized gas rotation velocities than the molecular gas in the outer part of the
rotation curve. In no case is the molecular gas rotation velocity measurably
lower than that of the ionized gas. We suggest that the lower ionized gas
rotation velocity can be attributed to a significant contribution from
extraplanar diffuse ionized gas in a thick, turbulence supported disk. Using
observations of the H$\gamma$ transition also available from CALIFA, we measure
ionized gas velocity dispersions and find that these galaxies have sufficiently
large velocity dispersions to support a thick ionized gas disk. Kinematic
simulations show that a thick disk with a vertical rotation velocity gradient
can reproduce the observed differences between the CO and H$\alpha$ rotation
velocities. Observed line ratios tracing diffuse ionized gas are elevated
compared to typical values in the midplane of the Milky Way. In galaxies
affected by this phenomenon, dynamical masses measured using ionized gas
rotation curves will be systematically underestimated.
