Whether you want the dash inside or outside quotation marks when there is an interruption is really a matter of personal preference.
When the quote is interrupted, you might decide to put the dash inside. If your thinking is that the dash is not part of the original quote, then put the dash outside the quotes.
Just be consistent. If you put it inside when the quote ended, put it inside when/if the quote begins again.
...on the side of the -- " this is exactly what he said " -- roadway as if he...
...on the side of the" -- this is exactly what he said -- "roadway as if he...
Happy punctuating!
Margie