The existence of inverted hysteresis loops (IHLs) in magnetic materials is still in debate due to the lack of direct evidence and convincing theoretical explanations. Here we report the direct observation and physical interpretation of complete IHL in Ni45Fe55 films with 1 to 2 nm thin Ni3Fe secondary phases at the grain boundaries. The origin of the inverted loop, however, is shown to be due to the exchange bias coupling between Ni45Fe55 and Ni3Fe, which can be broken by the application of a high magnetic field. A large positive exchange bias (HEB = 14 × HC) is observed in the NiFe composite material giving novel insight into the formation of a noninverted hysteresis loop (non-IHL) and IHL, which depend on the loop tracing field range (HR). The crossover from non-IHL to IHL is found to be at 688 Oe.