Flash memories are the preferred choice for data storage in portable gadgets. The charge trapping nonvolatile flash memories are the main contender to replace standard floating gate technology. In this work, we investigate metal/blocking oxide/high-k charge trapping layer/tunnel oxide/Si (MOHOS) structures from the viewpoint of their application as memory cells in charge trapping flash memories. Two different stacks, HfO2/Al2O3 nanolaminates and Al-doped HfO2, are used as the charge trapping layer, and SiO2 (of different thickness) or Al2O3 is used as the tunneling oxide. The charge trapping and memory windows, and retention and endurance characteristics are studied to assess the charge storage ability of memory cells. The influence of post-deposition oxygen annealing on the memory characteristics is also studied. The results reveal that these characteristics are most strongly affected by post-deposition oxygen annealing and the type and thickness of tunneling oxide. The stacks before annealing and the 3.5 nm SiO2 tunneling oxide have favorable charge trapping and retention properties, but their endurance is compromised because of the high electric field vulnerability. Rapid thermal annealing (RTA) in O2 significantly increases the electron trapping (hence, the memory window) in the stacks; however, it deteriorates their retention properties, most likely due to the interfacial reaction between the tunneling oxide and the charge trapping layer. The O2 annealing also enhances the high electric field susceptibility of the stacks, which results in better endurance. The results strongly imply that the origin of electron and hole traps is different—the hole traps are most likely related to HfO2, while electron traps are related to Al2O3. These findings could serve as a useful guide for further optimization of MOHOS structures as memory cells in NVM.