Spectographically determine surface composition of exoplanet
By the title of your question, I don't know if you're asking about the surface composition or the bulk composition. I will answer both.
Although spectrometry can be used to determine the atmosphere composition of a planet, it might also, in theory, helps us to determine the composition of the surface using, as you said it, the reflected light of the planet. This can be done in Solar System planets or moons, because detecting the reflected light is hard but still feasible. In exoplanets tho, it's still very complicated. Maybe with the James Webb Telescope it may be possible in the future. In fact, there are certain papers from which the process of differentiating oceans from land in exoplanets is described, such as Ford et al. (2001), Cowan et al. (2009) or Kawahara and Fujii (2010). I suppose that the actual composition may also be possible. They use the rotation of the planet combined with the difference of spectrometry to make a mapping of the theoretical surface of an Earth-like planet.
Nonetheless, I doubt it about the bulk composition, basically because as you pointed it,  light can't reach into the Interior of a planet, so it's impossible to study its spectrometry in that regard.
If you want to know about the bulk composition of an exoplanet, for example, you can use other techniques such  as the mass radius relationship, which can be often used to determine its bulk composition. Look at Zeng and Sasselov (2013), for example.