The structure and kinematics of gaseous, disk-halo interfaces are imprinted with the processes that transfer mass, metals, and energy between galactic disks and their environments. We study the extraplanar diffuse ionized gas (eDIG) layer in the interacting, star-forming galaxy NGC 5775 to better understand the consequences of star-formation feedback on the dynamical state of the thick-disk interstellar medium (ISM). Combining emission-line spectroscopy from the Robert Stobie Spectrograph on the Southern African Large Telescope with radio continuum observations from Continuum Halos in Nearby Galaxies - an EVLA Survey, we ask whether thermal, turbulent, magnetic field, and cosmic-ray pressure gradients can stably support the eDIG layer in dynamical equilibrium. This model fails to reproduce the observed exponential electron scale heights of the eDIG thick disk and halo on the northeast ($h_{z,e} = 0.6, 7.5$ kpc) and southwest ($h_{z,e} = 0.8, 3.6$ kpc) sides of the galaxy at $R < 11$ kpc. We report the first definitive detection of an increasing eDIG velocity dispersion as a function of height above the disk. Blueshifted gas along the minor axis at large distances from the midplane hints at a disk-halo circulation and/or ram pressure effects caused by the ongoing interaction with NGC 5774. This work motivates further integral field unit and/or Fabry-Perot spectroscopy of galaxies with a range of star-formation rates to develop a spatially-resolved understanding of the role of star-formation feedback in shaping the kinematics of the disk-halo interface.