One of the best methods for mic'ing an acoustic guitar is with one or more condenser mic's, their sensitivity makes them great for picking up the rich frequencies of your guitar.
But in our live band scenario that's not going to work because they will be picking up too much of the unwanted spill from the sound of the other instruments playing, and nobody will be able to hear the guitar while they're playing live. But there are other ways you can record your acoustic guitar in a live band, providing it can be plugged in with a soundhole pickup or piezo system installed.
Mic'ing an acoustic combo and using DI
If you have an acoustic combo you could try mic'ing with one or two mic's trying different positions in the same way as the guitar amps in the previous episode. But some acoustic combos also offer XLR output to run a signal straight to the interface for recording. This will allow greater control in the mixing stage while allowing the amplifier to be heard during the performance by the musicians.
You could also use a splitter box to get a DI signal of the acoustic guitar from a PA too.
Recording an acoustic guitar plugged into an amp or PA is always a compromise tonally, it won't sound as harmonically full as mic'ing the guitar itself because your piezo pickup under the guitar's bridge saddle or soundhole pickup is responsible for a large part of the sound. Some soundhole pickups also take vibrations from the guitar's soundboard to help convey a more natural sound, but there's sometimes a slight metallic nature to the sound.
With piezos, their sonic character can sometimes lead to a brittle harsh tonality referred to as 'quack'. There are preamp systems installed in some electro acoustics that help address this through onboard three-band EQ, but there are also EQ and preamp pedals available that can help you achieve a smoother more acoustic-natured sound when amplified. And that could be an especially wise investment for live recording as well as performances. Inevitably though, you may need to balance a desire for a richer acoustic sound with bottom end with enough mid and treble in the tone for your acoustic to stand out in a band mix and for you to hear it well enough in the live performance. As always, don't be afraid to change your sound to achieve the best results for this live session.
Finally, it's a fundamental point but it bears repeating; you need to make sure all your guitars are in tune throughout the session. The guitarists and bassist should have already invested in a decent tuner pedal for playing live anyway, but make sure you regularly check that you're in tune while recording because repeated playing and changes in room temperature can all have an effect on instrument intonation.