This paper presents the first reliable physical-layer network coding (PNC) system that supports real TCP/IP applications for the two-way relay network (TWRN). Theoretically, PNC could boost the throughput of TWRN by a factor of 2 compared with traditional scheduling (TS) in the high signal-to-noise (SNR) regime. Although there have been many theoretical studies on PNC performance, there have been relatively few experimental and implementation efforts. Our earlier PNC prototype, built in 2012, was an offline system that processed signals offline. For a system that supports real applications, signals must be processed online in real-time. Our real-time reliable PNC prototype, referred to as RPNC, solves a number of key challenges to enable the support of real TCP/IP applications. The enabling components include: 1) a time-slotted system that achieves us-level synchronization for the PNC system; 2) reduction of PNC signal processing complexity to meet real-time constraints; 3) an ARQ design tailored for PNC to ensure reliable packet delivery; 4) an interface to the application layer. We took on the challenge to implement all the above with general-purpose processors in PC through an SDR platform rather than ASIC or FPGA. With all these components, we have successfully demonstrated image exchange with TCP and twoparty video conferencing with UDP over RPNC. Experimental results show that the achieved throughput approaches the PHYlayer data rate at high SNR, demonstrating the high efficiency of the RPNC system.