According to my instructor, 'every time' is used as an adjective + noun, 'there' is used as an adverb. But in the sentence below I think "every time" is used as a time expression adverb, and "there" is used as a pronoun.
But every time there's a thunderstorm around Marshfield, they say you can hear his rolling voice in the hollows of the sky.
But every time there's a thunderstorm around Marshfield, they say you can hear his rolling voice in the hollows of the sky.
Let's simplify the sentence to make it easier to analyse:
Every time there's a thunderstorm, you can hear his voice.
The phrase every time there's a thunderstorm is a temporal Adjunct (of frequency). Some grammars call Adjuncts "Adverbials". Notice that you can move this phrase around:
In terms of what kind of phrase this is, it's a noun phrase. The head noun is the word time. This noun has a Determiner, the word every. Determiners are words like the, a, my, this and so forth. The word time is also being modified by a restrictive relative clause there's a thunderstorm. We could rephrase the sentence like this:
The word there is the Subject of the clause there's a thunderstorm. It is analysed as a pronoun in modern grammars such as The Cambridge Grammar of the English Language (Huddleston & Pullum, 2002). There are many reasons why. One reason is that it is repeated in question tags at the end of sentences:
This is a different word from the locative word there that we see in sentences like I'll meet you there.
It seems then that the Original Poster is correct (apart from the small detail that every time ... is an Adverbial, but not an adverb - an adverb is always a single word).
As commented by Araucaria, the word "every" is not an adjective; it's a determiner.
I think when it's followed by "time", it functions as an adverbial phrase interchangeable with the adverb whenever.
As for the word "there", it's a pronoun used as a dummy subject to introduce or indicate the existence of the logical subject of the sentence (a thunderstorm).
Moreover, "Every time there's a thunderstorm" is an adverbial clause.
Mother to daughter: Every time (when) I go into the bath it's filthy. Liz Phair, song: Every time I see your face I get all wet between my legs.
I would say "every time when" is a three-part conjunction. "when" is mostly dropped.
As to the sentence type "There is a spot on your shirt" / "There is a God" the views are divided. Some say it is an adverb of place. The demonstrative character can fade away when "there" is used in existential sense. Some say "there" is the subject. That's the view of CGEL. Not my view.
For those who are interested in Liz Phair's song, here is the Link
