What you can’t do is to pause playback in Audacity while simultaneously continuing to record in Audacity (on one computer).
I presume that you want to do this in “real-time” (all in “one take”).
You could play a CD in a standalone CD player, via a mixer, with two microphones plugged into the mixer, and record from the mixer, but note that with a normal sound card you will only be able to record a maximum of two independent channels at the same time, which will limit what editing is possible after recording.
The “professional” way to do this would be to use a stand-alone CD player (or a second computer) to play the pre-recorded podcast, and run that, plus 2 microphones, via a mixer, and record on a machine that is able to record 3 (or more) independent tracks simultaneously. The recording machine could be a computer that has a multi-channel sound card, or a stand-alone recorder (such as a Zoom H4, Roland R-44, Boss BR-800, etc.) Note that some “multi-channel” sound cards and stand-alone recorders can play multiple tracks at the same time, but only record a maximum of 2, which is no good for this job.
The other “professional” approach is to “overdub”. That is, that you record all of the parts separately (usually you would work to a script to do this). The hardware requirements are much lower for this. All you need is a machine to record on (if using a computer, you will need to have a decent sound card - probably a USB sound card), a decent microphone, and a quiet place to record that is substantially free of echoes.
Don’t underestimate the importance of the “quiet place to record that us substantially free of echoes” - this is your “recording studio”. If you record in a kitchen, it will sound like you have recorded in a kitchen and not like a studio recording. If there is TV on in the background, that will be in the recording and there’s no way to remove it after the fact.
The most common problem that people make is that they assume that they can get a general purpose PC or Mac, and use it as an all-in-one recording studio. You can’t - a PC is not a recording studio, it is just a computer. A standard Windows PC has basically two audio pathways - stereo in and stereo out. For more than that you need additional hardware.