Sounds like you want to record live but have individual tracks of your instruments for play-back.
From what little i know... to do this in a live setting you need to have either (obvious)a multitrack recorder or a USB interface that will allow up to 6 or 8 individual tracks to be recorded at the same time. Even doing this you will not have isolated the instruments so there will be bleed from the other noise in the room when you play-back the individual tracks.
But you can get an interface that allows up to 8 tracks recorded live. The interface boxes start around 500 bones depending on brand and software pkg. you get with it. But you can easily drop a $1000.00 and up.
The interface boxes usually have XLR with phantom power and 1/4" TRS and (or) midi connections so you can run out of your board into the box as individual lines or just run the individuals directly into the interface.
But you need a powerful enough computer to run it properly as well.
MO-MONEY!!
I like the AVID products but there are plenty of choices. Definitely talk to some audio-heads at your neighborhood GC or Sam Ash.