Set a background color for several adjacent cells and “page”

I’m using a book style sheet but this question applies to standard notebook interface as well.

I’m writing a sequence of cells in different styles (text, equation, figure, figure caption, …) in a special section (e.g., "Example") and would like to color the background of all content in the Example. I group the cells, select that grouping bar and select Format>Background color to be pink (for example). This changes the background in each cell to be pink. Great!

Almost…

This procedure colors the background of the cells, but not of the "page" behind. This looks a bit choppy and ununified, as here:

two cells with same background color

Merging cells forces them to be the same style, which of course is not appropriate (as I have text, equations, …).

I’m seeking a way to color the background page as well, but of course just between the beginning and end of the chosen cells.

There are several questions here about setting the backgrounds of multiple cells with a single command, but none that I could find that colors the "page" as well.