Is it ever correct to put an exclamation mark together with the question mark? For example, "Why!?," he yelled, "that's so ridiculous!"?
As part of dialogue or a fictional work, yes.
I would avoid doing this in an academic paper, or outside of quotation marks.
The Interrobang was introduced by typographer Richard Isbell in 1966 (Typewriters with this glyph were briefly available in the late 1960s) as part of the Americana typeface. It was a combination of the question mark and the exclamation point. It never really caught on, though.