Recall that for a solid the work function is the amount of energy required to remove an electron from the solid. So for a solid that is modeled to have a constant potential in its interior and bounded by a potential related to the work function would look something like figure 2.3.1 in the following link:
A comparable, and better, schematic can be constructed by imagining bringing together many atomic potentials and would look like figure 1c here:
Energy Bands in Solids and Their Calculations
Note how between each atom, the potential bends over to connect to its neighbor's potential when added, thereby flattening the potential between them. So the electrons in the conduction band of a metal have energies that obviously sit below the work function level, but above the atomic potentials. The potential they see is very flat.
In general when atoms are brought together to construct a solid, the valence electrons will be enter into Bloch states which extend throughout the crystal, while the core electrons remain essentially localized. The core electrons do not show Bloch characteristics.
In a metal, simple calculations, such as the Wigner-Seitz method, show that the bottom of the conduction band sits a little below the energy barrier that exists between atoms. Note how the image in figure 1c referenced above has the bottom of the conduction band slightly below the energy barrier. But the state at k=0, which would be exactly at the bottom of the band, still has Bloch structure.
At the other end of the spectrum, crystals that have high ionic character, such as NaCl, the valence electrons do not show Bloch characteristics. The electronic structure of the ions is essentially a closed shell.
The valence electrons in solids that have more covalent bonding character will also have Bloch character, just like the valence electrons in a metal. Where these bands actually sit in relation to the barrier that exists between the atomic cores will likely vary from solid to solid. As in the metallic case, some part of the valence band will likely sit below the barrier between atomic cores.
An old text, but a good one, that discusses these points is J.M. Ziman's Principles of the Theory of Solids. Chapters 3 and 4.