Durability is a long-standing challenge in designing liquid-repellent surfaces. A high-performance omniphobic surface must robustly repel liquids, while maintaining mechanical/chemical stability. However, liquid repellency and mechanical durability are generally mutually exclusive properties for many omniphobic surfaces-improving one performance inevitably results in decreased performance in another. Here we report well-defined porous membranes for durable omniphobic surfaces inspired by the springtail cuticle. The omniphobicity is shown via an amphiphilic material micro-textured with re-entrant surface morphology; the mechanical durability arises from the interconnected microstructures. The innovative fabrication method-termed microfluidic emulsion templating-is facile, cost-effective, scalable and can precisely engineer the structural topographies. The robust omniphobic surface is expected to open up new avenues for diverse applications due to its mechanical and chemical robustness, transparency, reversible Cassie-Wenzel transition, transferability, flexibility and stretchability.