Spectographically determine surface composition of exoplanet We can determine the surface composition of a star by studying its spectrograph. If a exoplanet transits the star, then there is a slight change to the spectrograph, which lets us determine the composition of the planet's atmosphere.
When the planet just become visible from behind it's star, then the star's light will:-

come from the star (known composition)
travel through the planets's atmosphere (known composition)
reflect from the planet's surface (unknown composition)
travel through the planet's atmosphere again (known composition)

Is it possible (either currently, or theoretically) to use this method to determine the bulk surface composition of an exoplanet?
This might be very difficult to achieve as the light reflected from the planet will be swamped by direct light from the star.
How do astronomers determine the texture of an exoplanet? and Can visible wavelength spectroscopy study an exoplanet&#39;s chemical composition directly? might be releated
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.