Podcasting Using Multitrack

I have a podcast with 2 co-hosts, 3 people in total. I have an XLR mic and a mixer that goes into my PC. My co-hosts have an analog mic and are both in 2 separate locations. We record on Skype and it goes through my mixer into 1 audio channel.

Is it possible to record the 3 of us on 3 separate channels using Skype as well as multitrack in Audition? The ideal situation would be to have 3 separate channels on the multi-track for myself, 2nd mic, and 3rd mic. I'd want to record all 3 at the same time. Am I missing equipment? Could it be my settings? Is this even possible?

One solution is to record my audio and they record theirs separately on Audacity or some other program and I sync it up in post-production but it'd obviously be easier if we could record them all at once in 3 different channels.