How can we explain continuous absorption / emission?

[DomPhillips]

I am familiar with the explanations for atomic absorption and emission line spectra and how the existence of discrete, fixed energy levels can give rise to the absorption/emission lines that are seen at only very particular frequencies of EM radiation.
However, I have no intuitive understanding as to why the vast majority of objects that we see in the everyday world seem to absorb/reflect/transmit/emit EM radiation over a wide continuous frequency range. How can a black object absorb all wavelengths of visible EM radiation simultaneously? How can a white object reflect all wavelengths of visible light simultaneously? Is it actually a true continuous absorption or is it the absorption of innumerable different discrete frequencies which are very close together? What physical/atomic properties of a material govern which frequency ranges it absorbs in?Note:
I am familiar with how systems of delocalised electrons can give rise to absorption in the visible spectrum and how the absorption of IR can cause bonds to vibrate, but I am still none the wiser as to why these adsorptions always seem to be continuous (at least to an extent) and never perfectly discrete (as seems to be the case with line spectra).

 

[blue_leaf77]

This is because bulk medium consists of bonding of atoms/molecules, and the interaction with EM fields is governed by the collective behavior of those arrays of atoms/molecules called lattice instead of the individual atoms.

is it the absorption of innumerable different discrete frequencies which are very close together?

Yes it is and for which in crystalline materials, those very closely separated levels form the so called energy bands.