The current research developed a hybrid optical diagnostic method that combines laser absorption spectroscopy and high-speed schlieren for high-speed and spatiotemporally-resolved measurements of unsteady compressible flows. The diagnostic was demonstrated in measurements of an axisymmetric supersonic underexpanded jet seeded with molecular tracer (here in this study, CO \(_2\) ). By using a wavelength-tunable narrow-linewidth laser to probe the characteristic rovibrational absorption transitions of CO \(_2\) , the current study quantitatively determined the local pressure and temperature of the flow from the spectrally-resolved absorption data, at an effective measurement speed of 20 kHz. Meanwhile, a time-synchronized high-contrast schlieren imaging system captures the fine structures such as shock waves, the Mach disk, the triple points, the slip lines, and the jet boundaries in the underexpanded jet. The time evolution of the under-expanded jet structure under rapid background pressure change was measured, and key geometric parameters such as the Mach disk location and diameter were determined as functions of the back pressure. The current results were seen in good agreement with previous quasi-steady-state experiments, which verified the effectiveness of the current diagnostic.