Lightweight, durable waterproof and breathable membranes with multifunctional properties that mimic nature have great potential for application in high-performance textiles, efficient filtering systems and flexible electronic devices. In this work, the fluoride-free triblock copolymer poly(styrene-b-butadiene-b-styrene) (SBS) fibrous membrane with excellent elastic performance was prepared using electrospinning. According to the bionics of lotus leaves, a coarse structure was built onto the surface of the SBS fiber using dip-coating of silicon dioxide nanoparticles (SiO2 NPs). Polydopamine, an efficient interfacial adhesive, was introduced between the SBS fiber and SiO2 NPs. The hydrophobicity of the modified nanofibrous membrane was highly improved, which exhibited a super-hydrophobic surface with a water contact angle large than 160°. The modified membrane retained super-hydrophobic properties after 50 stretching cycles under 100% strains. Compared with the SBS nanofibrous membrane, the hydrostatic pressure and WVT rate of the SBS/PDA/SiO2 nanofibrous membrane improved simultaneously, which were 84.2 kPa and 6.4 kg·m−2·d−1 with increases of 34.7% and 56.1%, respectively. In addition, the SBS/PDA/SiO2 nanofibrous membrane showed outstanding self-cleaning and windproof characteristics. The high-performance fibrous membrane provides a new solution for personal protective equipment.