A photonics-based broadband microwave instantaneous frequency measurement (IFM) method is proposed by monotonously mapping the frequency to the slope of the time-varying phase of the microwave signal under test. This frequency-to-phase-slope mapping approach is realized utilizing a variable photonic delay line and a microwave photonic in-phase/quadrature (I/Q) mixer, where the I/Q mixer is composed of two phase modulators connected tail to tail within a fiber loop, an optical 90° hybrid, and a pair of low-speed balanced photodiodes. Thanks to the monotonous frequency-to-phase-slope mapping property, as well as the use of photonic delay line and microwave photonic I/Q mixing, the IFM system can achieve a wide-range frequency measurement without ambiguity. An experiment is performed. The established IFM system is able to operate from 5 to 67 GHz with a measurement error of less than 500 MHz, which achieves the widest frequency measurement range ever recorded by photonics-based IFM systems. In addition, the influences of the I/Q phase mismatch and the amplitude noise on the performance of the IFM system are also discussed. We believe that this photonics-based IFM system is a promising solution for wideband microwave frequency measurements.