My initial guess is yes there is a blackbody spectrum of photons inside a solid.
The process that emits thermal photons won't "know" that it is deep inside a solid and not near the surface, so the emission of thermal photons would be the same. They don't get very far.
So I'd like to ask: Is there a blackbody spectrum of photons inside a solid?
Let's assume that "inside" means in the center of a body with a temperature $T$ and that the body is at least several absorption lengths in size for photons near $k_BT$. Let's also assume the self-absorption is not so overwhelmingly strong that it significantly alters the emission process itself.
I believe that the answer will be the same for dielectrics, semiconductors and metals, but if the answer differs for these please mention it.