  We have obtained data for 41 star forming galaxies in the MUSE Atlas of Disks
(MAD) survey with VLT/MUSE. These data allow us, at high resolution of a few
100 pc, to extract ionized gas kinematics ($V, \sigma$) of the centers of
nearby star forming galaxies spanning 3 dex in stellar mass. This paper
outlines the methodology for measuring the ionized gas kinematics, which we
will use in subsequent papers of this survey. We also show how the maps can be
used to study the kinematics of diffuse ionized gas for galaxies of various
inclinations and masses. Using two different methods to identify the diffuse
ionized gas, we measure rotation velocities of this gas for a subsample of 6
galaxies. We find that the diffuse ionized gas rotates on average slower than
the star forming gas with lags of 0-10 km/s while also having higher velocity
dispersion. The magnitude of these lags is on average 5 km/s lower than
observed velocity lags between ionized and molecular gas. Using Jeans models to
interpret the lags in rotation velocity and the increase in velocity dispersion
we show that most of the diffuse ionized gas kinematics are consistent with its
emission originating from a somewhat thicker layer than the star forming gas,
with a scale height that is lower than that of the stellar disk.
