Silicon carbide (SiC) is a promising material for high-power electronic devices. Although SiO$_2$ dielectric film can be grown on SiC by conventional thermal oxidation, low channel mobility and poor gate oxide reliability are the critical issues for SiC power metal-oxide-semiconductor field-effect transistors (MOSFETs). In this work, we investigated the fundamental aspects of thermally grown SiO$_2$/4H-SiC structures such as an energy band alignment and flatband voltage (VFB) instability. Both electrical characterization and x-ray photoelectron spectroscopy (XPS) study revealed that a conduction band offset ($\Delta$E$_c$) between SiO$_2$ and SiC is extrinsically increased by large amount of negative interface charges. High-temperature hydrogen annealing could effectively passivate interface defects, but at the same time resulted in the reduced $\Delta$E$_c$ at SiO$_2$/SiC interfaces. We also found that intrinsic positive mobile ions exist in as-oxidized SiO$_2$/SiC structures. Post-oxidation annealing in Ar ambient mostly eliminates the mobile ions, but they are generated again by subsequent high-temperature hydrogen annealing despite the improved interface quality. These features were not observed for thermally-grown SiO$_2$/Si structures, and thus considered to be inherent to thermally grown SiO$_2$/SiC structures.