If you want to connect/distribute or publish two wifi networks at once, you need two cards. Plain and simple.
I've not run a configuration like this on my dual-wifi-nic laptop before, and though I have the feeling I've seen it said somewhere that you can't do it, I've no good reason to see why not. One frequently bridges two wifi connections on a FreeBSD device kicking around the LAN with success - problems may be a limitation of airbase/fake-ap.
Process is simple: Connect NIC 1 to wifi network. Start fakeap on NIC 2.