The phrase "a parallel narrative" is correct and usable in written English.
It can be used to describe a storyline that runs alongside another, often providing a different perspective or context to the main narrative.
Example: "The novel features a parallel narrative that explores the protagonist's childhood while the main story unfolds in the present."
Alternatives: "a concurrent storyline" or "an accompanying narrative".
There is also a parallel narrative about Einstein's theory of relativity.
Her forays into the town archives unearth a previous owner, Thatcher Greenwood, whose story unspools in a parallel narrative.
He hasn't so much constructed a parallel narrative, although, as ever in dance, personalities and relations are implied.
The trio of siblings of which Roger is the youngest provide a parallel narrative of hidden knowledge and difficult choices.
In what amounts to almost a parallel narrative, she sheds her academic skin, injecting biographical notes, lively anecdotes, insightful stories and interviews into her narrative.
It often acts as a parallel narrative to history: if you start digging with a textbook in your hand, you are soon going to get confused.
The doppelganger's career in propaganda movies is handled with deadpan humour, but we are kept off-balance by a piteous parallel narrative about imperial eunuchs and by the sheer horror of quotes from the tyrant's speeches.
They introduced an innovative parallel narrative about two (fictional) actors having an affair while working on the film, a self-referential device that echoed Fowles's literary stylistics.
Since then, the show has encompassed surreal live-action interludes, deep-cut big-screen homages and a post-apocalyptic parallel narrative that when taken together leaves "Animals" feeling like the strangest show on TV.
There's a welcome absence of parallel narrative.
Although the hook of the story is Xan's friendship with Duma, who quickly grows into a soccer-playing, motorcycle-racing wonderment, the parallel narrative is that of a child's inevitable, sometimes wrenching passage into adulthood.
