If you're going to copy two different drives to one backup drive you'll need to partition the backup drive so that it appears to be two separate drives. You can do that with the Disk Utility application that comes with the Mac OS.
Before you start using the backup drive use Disk Utility to create two partitions on it, one the same size as the internal drive of the Mini and the other with all the remaining space.
For instance, if you have a 1 TB drive as your backup and your Mini has a 160 Gb internal drive, create one 160 Gb partition on the backup drive to use as a clone of the Mini's internal drive and another partition that uses all the remaining space on the 1 TB drive. Theoretically that will be 840 Gb but in reality it will be somewhat less than that.
When you start up the backup drive it will show up as two separate drives, one the same size as your Mini's internal drive where you can clone the operating system and a second where you can backup your iTunes drive.