Pasting text and images together?

[David Epstein]

To clarify my original question:

I'm not expecting the built-in paste command to handle this task; I'm
wondering if I can script my own paste command to handle it.

Richmond, I can write a script to "paste" an image by itself (by creating
an image and setting its text to clipboardData["image"]).

But is there some way I can access both the text and the image that are on
the clipboard after I have copied a combination of those from, e.g., a web
browser?  (Pasting to Apple Notes confirms that the clipboard contains both
text and image.)