I'm having to bear losses because of my mother-in-law.
I suspect that whoever told you that meant to say that "because of" is a preposition phrase functioning as an adjunct (adverbial). In other words, they were combining function (adverbial) and category (PP) into the single term 'adverbial preposition phrase'.
Note that 'adverb' and 'adverbial' are not the same thing. The former is a word category (part of speech) while the latter is a function term (what words and phrases do).
Some modern grammars treat "because of" not as a complex preposition, but as a sequence of preposition + preposition phrase complement, though the adverbial function remains the same.
 I am [due a refund of about ten pounds].
 [Due to bad weather], the match was cancelled.
"Due" belongs to both adjective and preposition categories:
In  "due" is an adjective with a noun phrase complement. The bracketed adjective phrase functions as predicative complement of "be".
In  "due" is a preposition with a PP complement. The bracketed PP functions as a reason adjunct (adverbial).