The commercialization of portable zinc-air batteries has been limited due to issues related to the air cathode morphology. First, these types of batteries commonly use an aqueous electrolyte, which is susceptible to changes in air temperature and humidity that can cause leakage and block the air-cathode. This problem affects the oxygen reduction reaction and accelerates battery degradation. Second, there is only a non-rechargeable configuration due to the lack of an efficient bifunctional electrocatalyst capable to promote the oxygen reduction reaction and the oxygen evolution reaction. In this work, we developed a double layer TPU-CNT membrane to improve the oxygen diffusivity and to prevent electrolyte leakage. Two different foaming techniques were used to obtain a specific morphology. One membrane is hydrophilic with high absorption capabilities to prevent electrolyte leakage. The second membrane is hydrophobic, and it is used as the gas separation layer between the electrolyte and the exterior for improved oxygen diffusivity. The closed-cell membrane presented an optimal performance as a hydrophobic oxygen diffusion layer, whereas the hydrophilic open-cell membrane, apart from increasing the catalytic surface area, also increased the water absorption by 12 times, with a swelling capacity of 68%. Within the hydrophilic membrane, we developed a bifunctional electrocatalyst to achieve an electrically rechargeable configuration. The electrocatalyst was fabricated with Co3O4 particles attached to a nitrated carbon support. The functionalized carbon matrix improves not only the carbon wettability but also provides acidic sites and carbon-containing functional groups. The electrochemical characterization demonstrated lower overpotential and higher stability over 160 cycles for the Co3O4 catalyst attached to the nitrated carbon matrix compared to the pristine carbon matrix. The electrochemical characterization demonstrated lower overpotential, higher stability, and lowe