A three-oxide sodium borosilicate glass was irradiated with 2.3 MeV electrons up to 0.15 GGy and 4.6 GGy, and subsequently with 96 MeV Xe ions. The irradiated samples were characterised using Raman spectroscopy, ToF-SIMS, microhardness and surface profilometry. Electron irradiation of the pristine glasses resulted in different structural modifications at the sample surface and in the bulk of the glass, whereas, ion irradiation of either the pristine or bulk of the electron pre-irradiated glasses induced same structural, physical and mechanical property changes. Furthermore, sample surfaces showed a different behaviour than that of the bulk upon subsequent ion irradiation. These results show that the radiation sensitivity of surfaces can significantly vary depending on the type of the irradiation. Therefore, detailed studies aimed at understanding the response of the surfaces to mono and electron-ion double-beam irradiations should be undertaken to address the long-term evolution of the nuclear waste glass matrix surfaces.