I think Evgeniy's comment contains an interesting remark: the expression "nel mezzo di" corresponds (literally) to saying "in the middle of" in English. As in the English version, middle/mezzo in this expression is a noun, with meaning "the point at an equal distance from the edges or ends of something", where the something is specified by what follows "di" in Italian, and "of" in English.
This similarity carries over only partially, because as far as I know there's no expression corresponding to "nel bel mezzo di" in English. However, the modification with the attribute "bel" in Italian is peculiar to the expression (you wouldn't be able to substitute "bel" with adifferent adjective), and "bel" doesn't modify the meaning of the expression, so in some sense it's emptied of its attributive meaning.
In the expression "nel bel mezzo di" we see how a sentence which was a functional part of the speech ("in" + (attribute) + noun + "di" + noun) became a static expression with a specific attribute, and in some sense rigidified to one single prepositional unit "nel bel mezzo di".
The expression "in mezzo a" seems closer to the preposition "amid/mid" which is now present mostly only in literary English. It has the same meaning as "nel mezzo di" and it's morphologically similar (just like "middle" is related to "mid" in English), however it seems to be a slightly different construction.
Unfortunately, I don't know a source explaining this and providing other examples of "sentences which become prepositional expressions", it would be interesting to see a systematic explanation of this.