Unfortunately computer recording software, including Audition, isn't designed to work with more than one audio interface at the same time. The correct way to do this is to use an external USB interface with two mic inputs into the one device. This can just be a low cost USB interface with two mic inputs or even, these days, some fairly low cost mixers with USB connection.
There is a possible work around using ASIO4All. But it is not straight forward to set up and won't do your recorded audio quality any good I'm afraid.
ASIO4ALL - Universal ASIO Driver For WDM Audio