We present spectral analysis of ASCA observations of the early-type galaxies NGC 720 (E4) and NGC 1332 (E7/S0) with emphasis on constraining the relative contribution to the X-ray emission from hot gas and the integrated emission from X-ray binaries. Single-temperature spectral models yield poor fits to the spectrum (chi(red)(2) similar to 3) over the similar to 0.5-5 keV energy range. Two-temperature models significantly improve the spectral fits (chi(red)(2) similar to 1.5) and have soft-component temperatures and subsolar abundances consistent with previous ROSAT single-temperature models (T(soft)similar to 0.6 keV, abundances similar to 0.1) and hard-component temperatures (T(hard)greater than or similar to 3 keV) consistent with those expected from a discrete component. The soft component dominates the emission in both galaxies, especially in the 0.4-2.4 keV band used in previous ROSAT studies: flux ratios are F-hard/F-soft = 0.19(0.16-0.45) for NGC 720 (2 sigma) and F-hard/F-soft = 0.31(0.24-0.55) for NGC 1332 (90%). Combining these spectral results with ROSAT data we updated constraints on the mass distributions for NGC 720 and NGC 1332. For NGC 720, which yields the more precise constraints, the ellipticity of the intrinsic shape of the mass is slightly reduced (Delta epsilon(mass)approximate to 0.05) when the discrete component is added, epsilon(mass)similar to 0.4-0.6 (90%). The estimates for the total mass increase with increasing discrete flux, and we find that models with F-hard/F-soft = 0.45, the 2 a upper limit,have masses that exceed by similar to 30%-50% those where F-hard/F-soft = 0.