In this Letter, we report a wideband and low-error photonic instantaneous frequency measurement (IFM) system for microwave signals, which uses a nonlinear interferometer constructed with cascaded degenerate four-wave mixing (FWM) and in-between dispersion to introduce a tunable time delay. The microwave frequency is interpreted through interference of two idlers generated in cascaded FWM stages. This new approach allows parallel implementation of multiple IFMs without an overlap of idler wavelengths used for different IFMs, which is crucial to realize a wide frequency coverage and high accuracy without compromising the system practicality. A large, 40 GHz measurement bandwidth and a low measurement error of approximately 0.4% have been successfully achieved.