Honestly, I don't know, as I've never tried to do anything like this. However, Audacity does allow for multitrack recording, so even if one cannot do what you describe all in one go, (and it may, give it a try!), one can still record the streaming internet content using Audacity w/Soundflower (and Soundsource, not necessary, but helpful in switching input and output sources quickly and easily). After the streaming content is recorded on one track, you could record your own commentary track separately on another track. As I don't know whether you can hear the track that's playing as you're recording over it, you could draft your comments in script form and record them cold, then use the "Timeshift" tool in Audacity to move them back and forth until they're placed where you like, relative to the already recorded audio material they're meant to supplement and comment on. Then, on playback, you'll hear the original streamed internet content you recorded with your own comments interpolated where you want them to be.
I recommend anyone wanting to do various tasks with Audacity to refer to their user's manual and tutorials, located on their webpage. Here's a link to their Tutorials: http://audacityteam.org/wiki/index.php?title=Tutorials
Here's a link to their online manual: http://audacityteam.org/help/documentation
From the manual, here's a page with a tip on recording two audio sources. It does seem to require equipment other than just Audacity: http://audacityteam.org/manual-1.2/tuto ... _ed_1.html
And read over their Wiki page...that's where I found the information I posted above about using Soundflower with Audacity. There's lots of information available on Audacity's web resources.
Obviously, there is software out there that will allow you to do this or even more ambitious things more readily, perhaps, than Audacity, but they cost money. One such is the new Wiretap Anywhere, which costs $129.00. Audacity is free and thus may not offer every bell and whistle one would prefer, but if "free" is the right price, then I think one can do pretty much anything with Audacity, just using a bit of ingenuity and effort and time. Good luck!