Hum, I'm no alsa expert, but as I understand you need to configure it in a specific way if you want to use multiple audio sources.
I've seen pulseaudio mentioned a number of times in that context, whether or not that is a requirement as opposed to a convenience I'm not sure.
Either way, it's not really a hardware issue - it should definitely be possible to send audio from multiple applications. I would hit the alsa doc and see if you can makes heads or tail of it.