Dispersion plays a major role in the behavior of light inside photonic devices. Current state-of-the-art dispersion measurement techniques utilize linear interferometers that can be applied to devices with small dispersion-length products. However, linear interferometry often requires beam alignment and phase stabilization. Recently, common-path nonlinear interferometers in the spontaneous regime have been used to demonstrate alignment-free and phase-stable dispersion measurements. However, they require single-photon detectors, resulting in high system cost and long integration times. We overcome these issues by utilizing a nonlinear interferometer in the stimulated regime and demonstrate the ability to measure the dispersion of a device with a dispersion-length product as small as 0.009 ps/nm at a precision of 0.0002 ps/nm. Moreover, this regime allows us to measure dispersion with shorter integration times (in comparison to the spontaneous regime) and conventional optical components and detectors.