A family of Microsoft word processing software products for creating web, email, and print documents.
Alice, you would have to separate that page from the preceding one with a section break (probably a Next Page break is simplest) and turn off the Link to Previous in the new page's header. Then insert two rectangles anchored in the header, one sized and positioned to cover the top half of the page and the other to cover the bottom half. Fill each rectangle with the desired color for that part of the page.
If the part at the bottom of the page continues onto the next page, you'll need another section break and a full-page rectangle in that section's header, again unlinked from previous.
The drawback is that text can't flow across section breaks. That means you shouldn't insert the section breaks until the document is complete and won't be edited any more -- or else you might find that a section pushes one or more lines to a new page, then the section break forces another new page, and you're left with a mostly-blank page.
To answer your question about "no header or footer in the middle of a page", if you insert a Continuous section break in the middle of the page, the second section's header and footer do exist (in the software) but they're hidden; the header and footer that appear on the page are both from the earlier section. For the purpose of displaying a rectangle anchored in the header, the answer is "they might as well not exist there because you can't see the rectangle".