I'm not aware of a word that would specify textual content that lies between successively numbered chapters. I don't believe people think of it this way when they layout books of fiction.
There are two ways to consider this.
1. Your content is the last section of Chapter 2 or the first section of Chapter 3.
In this case you would call it a section. Different formatting might make it appear like it is set off from the chapters.
My e-book version of Frank Herbert's Dune uses this technique. Excerpts from a book, "Manual of Muad'dib," provide lead-in text for every chapter. The text is indented like a quote, then the chapter text follows. So, in this case the text of interest is the first section of the chapter.
2. Your content is a chapter without a heading (or with a heading if you prefer)
My e-book version of Jeff Wheeler's The Druid uses this technique. Between successively numbered chapters he has text that is a journal entry from another point of view. It is treated like a chapter and begins on a new page like chapters. It has no heading. In the table of contents, this in-between chapter appears with the first few words of the text rather than a chapter title. But it has no number.
In my e-book version of Dan Brown's Origin, he includes short news segments (as you are wanting to do) as their own numbered chapter.
While you are free to do whatever you want, when it comes to laying out the actual book, you will probably be required to choose one of these approaches: treating your in-between content as a chapter section or as a chapter on its own.