We demonstrate that a dual frequency comb-transient absorption (DFC-TA) technique can be combined with a time-domain interferometric detection to measure both the transient absorption and refraction spectra of molecules in solution. To do this, the pump-probe signal field of DFC-TA is allowed to interfere with a time-delayed local oscillator field in a time domain. We show that this DFC interferometric pump-probe spectroscopy (DFCIPS) technique has a unique ability to extract the phase and amplitude information on the pump-probe signal using just a single-scan data, while conventional techniques require an independent signal measured without the pump field for the normalization of the pump- probe spectrum. As a proof-of-principle experiment, we here show that the DFC-IPS enables us to simultaneously measure the frequency-resolved (from 650 to 950 nm) transient absorption and refraction signals with an exceptionally broad dynamic range from femtosecond to nanosecond without using a mechanical translational stage for pump-probe time-scanning. We anticipate that our DFC-IPS technique with femtosecond time-resolution capability will be useful to investigate photoinduced chemical and biological reactions covering broad dynamic ranges.