It's technically possible, but logistically difficult. The path to public release is very different between novels and movies - as @Laurel notes, even official novelizations often suffer from too-fast turnarounds, lack of information, and script changes. Essentially, a novel is considered "final" at a very different point in its publication cycle than a movie is. In order to make a complementary book-movie pair, you would need to drastically change the manner and timelines in which both are produced - a process which is complicated by the sheer number of people, studios, and companies involved.
For example, you're probably familiar with the improvised scene in Raiders of the Lost Ark, where instead of the planned dramatic fight scene between Indy and the Arab swordsman, Indy simply pulls his gun and shoots the guy. Now consider: if you were trying to write a companion novel based off the script, you might have already written the big dramatic fight, which now needs to be cut. That sounds simple enough, but what if that change had happened on the last day of shooting, when the novel is finished and out of the author's hands?
What if the change had been more complex? For example, Han Solo's "I know" to Leia was improvised. What if an entire chapter of the novelization was devoted to Leia's inner monologue coming to terms with his original line ("I love you too"), and now needs to be completely rewritten? Again, possible, but logistically very difficult.
There's also the matter of the huge difference between the kinds of stories books tell, and the kinds of stories movies tell. One of the most important things I learned when getting my screenwriting degree was the following: Books tell stories through thoughts, stage plays tell stories through dialogue, and movies tell stories through action.
This is obviously not to say you can't have action in books, or thoughts in movies, but books are far better suited to sharing characters' inner thoughts and feelings with the reader than a movie is. A movie is much better at conveying action sequences than a book is. A Hollywood action sequence might take five minutes on screen, but showing the same amount of content in a novel might take fifty pages or more. A subtle character arc can take place over 500 pages of a novel, but feel abrupt and on-the-nose in a 90-minute movie. In theory, this sounds like it ought to support your idea of a book/movie pair meant to supplement each other - but if you look at novelizations of movies, and movies made from books, you start to quickly see pitfalls.
Novelizations often suffer from a lack of depth, as the stories of the movies they're describing are both not long enough for a traditional novel (incidentally, this is why short stories make better movies than novels do), and not internal enough. The story told in the movie typically isn't concerned with the inner thoughts and feelings of its characters, and it's hard to post-facto create enough of those thoughts & feelings to fill a novel.
Likewise, movies made from books are frequently criticized for leaving out massive and important parts of the book, as well as mangling characters. Movies simply don't have the space to tell the same scale of story as a novel, and likewise cannot easily show character depth (at least not without using gimmicks like voiceovers).
Essentially, books and movies are designed to tell very different kinds of stories at very different scales. It's possible to turn one into the other, but the translation is almost never perfect and much is often lost. Combined with the logistical difficulties of creating an interlinked book/movie pair, it means doing so is generally not worth the time, effort, and cost when instead you could produce a great standalone movie or novel.
Therefore, in order to make this happen, the publisher and producer would have to carefully coordinate their respective final products from concept to release. It would require extensive cooperation and planning, and would likely only be undertaken for a very, very well-known property, or a writer or director/producer/star who is popular enough to be worth the risk. And it would need a story which contains enough inner thoughts/feelings/character development and enough external action to benefit from the dual format.