We present a comprehensive study of interstellar X-ray extinction using the extensive Chandra supernova remnant (SNR) archive and use our results to refine the empirical relation between the hydrogen column density and optical extinction. In our analysis, we make use of the large, uniform data sample to assess various systematic uncertainties in the measurement of the interstellar X-ray absorption. Specifically, we address systematic uncertainties that originate from (i) the emission models used to fit SNR spectra; (ii) the spatial variations within individual remnants; (iii) the physical conditions of the remnant such as composition, temperature, and non-equilibrium regions; and (iv) the model used for the absorption of X-rays in the interstellar medium. Using a Bayesian framework to quantify these systematic uncertainties, and combining the resulting hydrogen column density measurements with the measurements of optical extinction toward the same remnants, we find the empirical relation N-H = (2.87 +/- 0.12) x 10(21) A(V) cm(-2), which is significantly higher than the previous measurements.