We present Far Ultraviolet Spectroscopic Explorer and Hubble Space Telescope observations of high , intermediate , and low ion absorption in high-velocity cloud Complex C along the lines of sight toward five active galaxies . Our purpose is to investigate the idea that Complex C is surrounded by an envelope of highly ionized material , arising from the interaction between the cloud and a hot surrounding medium . We measure column densities of high-velocity high ion absorption , and compare the kinematics of low , intermediate , and high ionization gas along the five sight lines . We find that in all five cases , the H i and O vi high-velocity components are centered within 20 km s ^ { -1 } of one another , with an average displacement of < \bar { v } _ { \mathrm { O~ { } VI } } - \bar { v } _ { \mathrm { H~ { } I } } > = 3 \pm 12 km s ^ { -1 } . In those directions where the H i emission extends to more negative velocities ( the so-called high-velocity ridge ) , so does the O vi absorption . The kinematics of Si ii are also similar to those of O vi , with < \bar { v } _ { \mathrm { O~ { } VI } } - \bar { v } _ { \mathrm { Si~ { } II } } > = 0 \pm 15 km s ^ { -1 } . We compare our high ion column density ratios to the predictions of various models , adjusted to account for both recent updates to the solar elemental abundances , and for the relative elemental abundance ratios in Complex C. Along the PG 1259+593 sight line , we measure N ( Si iv ) / N ( O vi ) = 0.10 \pm 0.02 , N ( C iv ) / N ( O vi ) = 0.35 ^ { +0.05 } _ { -0.06 } , and N ( N v ) / N ( O vi ) < 0.07 ( 3 \sigma ) . These ratios are inconsistent with collisional ionization equilibrium at one kinetic temperature . Photoionization by the extragalactic background is ruled out as the source of the high ions since the path lengths required would make HVCs unreasonably large ; photoionization by radiation from the disk of the Galaxy also appears unlikely since the emerging photons are not energetic enough to produce O vi . By themselves , ionic ratios are insufficient to discriminate between various ionization models , but by considering the absorption kinematics as well we consider the most likely origin for the highly ionized high-velocity gas to be at the conductive or turbulent interfaces between the neutral/warm ionized components of Complex C and a surrounding hot medium . The presence of interfaces on the surface of HVCs provides indirect evidence for the existence of a hot medium in which the HVCs are immersed . This medium could be a hot ( T \gtrsim 10 ^ { 6 } K ) extended Galactic corona or hot gas in the Local Group .