Perhaps you could follow this style:
He said:
> -- Hello, Lisa.
> -- Hi, Peter!
> -- How things are going on?
> -- Fine, thank you.
Please note that, after the > symbol, there are two dashes (--), which are transformed into an em-dash by Multimarkdown. Likewise, finish each line with two spaces (invisible in the above code) to insert a line break.
Juanjo