I've only done a small amount of tinkering on regular expressions, in regards to the site. Going for the [u] and [/u] style of underline, I did this quick:

[url=http://regex101.com/r/cN1vS4]Underline Code[/url]

I'm guessing it may not need things like the /mg (multi-line and global tag), looking at some of the other code. It goes off of the asterisk style of formatting rather than the hider and quote types. It also doesn't seem to work if I enter to a new line, my guess being that it's because the code doesn't try to match/capture new line.