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Accurate knowledge of the intrinsic optical properties of 3D printing materials, i.e., spectral absorption and scattering coefficients, phase function, and refractive index, is essential for simulating the appearance of translucent prints on displays (softproofing) or optimizing material arrangements to achieve desired optical effects in multi-material 3D prints. This information is also critical for designing printing materials that mimic the optical characteristics of other materials, a key requirement in applications like dental restorations. Current methods for measuring these properties rely on specialized laboratory equipment and expert knowledge. In this paper, we propose an approach that uses a commercial reflectance/transmittance spectrophotometer to determine the spectral absorption and scattering coefficients and refractive index of 3D printing materials. We model the light path of this device to simulate reflectance and transmittance measurements via a Monte Carlo path tracer. We then predict measurements for a large set of random but plausible intrinsic optical material properties for three different sample thicknesses. With these data, we train machine learning models to infer the intrinsic properties from phenomenological reflectance/transmittance measurements, considering a priori knowledge of smoothness as a regularization constraint. We validate our method by comparing results for real printing materials with accurate laboratory measurements and provide the trained machine learning models to the community.