I'm not sure if I follow you. I assume you are recording your whole band live…correct? If so, a muti-channel interface is absolutely necessary in order to assign each input (instrument) to a specific track. You have a choice as to what signal format you want to send your AxeFX channel(s) into that interface. You can go in as stereo audio, (using balanced or unbalanced), or S/PDIF, digital. But again…you need a muti-channel interface. There are many on the market and the more channels, the higher the cost (and capability) Some will even do digital format conversions. I use a MOTU 828 with ProTools. If you are recording ONLY your guitar, fine! No problem.
The bottom line is; The AxeFX is a digital Guitar processor with D/A audio outputs FIRST. It can be used as an "interface" for a lot of things such as playing MP3 music from your computer into a home stereo system, but when it come to simultaneous multitrack recording, it's just another signal source.