Context. A recent discovery of two stellar clusters associated with the diffuse high-latitude cloud HRK 81.4-77.8 has important implications for star formation in the Galactic halo. Aims. We derive a plausible distance estimate to HRK 81.4-77.8 primarily from its gaseous properties. Methods. We spatially correlate state-of-the-art HI, far-infrared and soft X-ray data to analyze the diffuse gas in the cloud. The absorption of the soft X-ray emission from the Galactic halo by HRK 81.4-77.8 is used to constrain the distance to the cloud. Results. HRK 81.4-77.8 is most likely located at an altitude of about 400 pc within the disk-halo interface of the Milky Way Galaxy. The HI data discloses a disbalance in density and pressure between the warm and cold gaseous phases. Apparently, the cold gas is compressed by the warm medium. This disbalance might trigger the formation of molecular gas high above the Galactic plane on pc to sub-pc scales.