The use of amorphous GeSe-based chalcogenides in ovonic threshold switching selectors for highly efficient phase-change memory devices involves the formation of contacts with metal electrodes, where the nature of interfacial contact plays a crucial role in controlling the power efficiency. Here, by using a joint experimental-theoretical approach we study the key contact properties between TiN-electrode and amorphous GeSe (a-GeSe) semiconductor. Two types of stackable devices with and without amorphous carbon (a-C) interlayer film were investigated; namely, TiN/a-GeSe and TiN/a-C/a-GeSe stacks. The interfacial contact between TiN electrode and a-GeSe is characterized by a high Schottky barrier height (SBH) type contact. The insertion of the Carbon buffer layer develops a lower SBH with a-GeSe, leading to a higher leakage current and a lower VTH, in line with the experimental observation.