Massive developed discontinuities are the salient geological features of unconventional oil and gas reservoirs, and the hydraulic fractures’ capabilities of crossing the discontinuities concern the stimulation effects of hydraulic fracturing. To study the development of the fracture process zone (FPZ) when the hydraulic fracture orthogonally propagates through a discontinuity, the self-designed visual fracturing equipment was adopted to carry out hydraulic fracturing tests on sandstone plates with a prefabricated unbounded friction interface. Based on the digital image correlation method, the displacement and strain characteristics during the hydraulic fracture propagation across the orthogonal interface were monitored in real time. The test results show that the FPZ has developed across the interface before the hydraulic fracture extends across the interface. Whether the fracture can propagate through the interface is predetermined at the initial developmental stage of the FPZ and is not affected by the stress-softening process in the FPZ. Based on the Renshaw-Pollard criterion, a criterion considering the FPZ boundary was established for estimating the fracture propagation across the friction interface, and it was verified by test data and existing results. In comparison, the improved criterion considers a more accurate application scope of elastic fracture mechanics at the fracture front. The aspect ratio of the FPZ has a significant effect on the improved criterion, and the lower limit of friction coefficient required for the fracture propagation orthogonally across the interface declines as the aspect ratio of the FPZ rises under the same conditions.