Quantifying light transport in turbid media is a long-standing challenge. This challenge arises from the difficulty in experimentally separating unscattered, ballistic light from forward scattered light. Correlation gating is a new approach that numerically separates light paths based on statistical dynamics of the optical field. Here we apply correlation gating with interferometric near-infrared spectroscopy (iNIRS) to separate and independently quantify ballistic and scattered light transmitted through thick samples. First, we present evidence that correlation gating improves the isolation of ballistic light in a thick, intrinsically dynamic medium with Brownian motion. Then, from a single set of iNIRS transmission measurements, we determine the ballistic attenuation coefficient and group refractive index from the time-of-flight (TOF) resolved static intensity, and we determine the reduced scattering and absorption coefficients from the diffusive part of the TOF resolved dynamic intensity. Finally, we show that correlation gating is applicable in intrinsically static media in which motion is induced externally. Thus, for the first time, to the best of our knowledge, the key optical properties of a turbid medium can be derived from a single set of transmission measurements.