You've made no talk of hardware or software, so its difficult to discuss specific issues, but there's no fundamental reason why you cannot mix and match different types of RAID on the same server platform.
In fact, its quite desirable to do so; its quite a common configuration option for some types of server to contain different types (speeds/capacities) of drive, striped in different ways, for different tasks (note I'm NOT talking about having different speeds of drive or so-on in the same RAID container/group/set/bunch of disks, but of having more than one RAID group)
On a database server, for example, DB log files might need very fast write speed above all else, and so you'd choose a RAID system that favours that; main database files may require a more balanced choice between read and write so again, you'd choose a RAID system that gave you that, DB backup files could be saved to slower/cheaper/higher capacity drives, etc.
In the example you describe, again its not that unusual to have different RAID sets that are home to totally different sets of data on a file server.
Of course, if you do this then you've made it much more complicated to maintain the hardware platform - its no longer enough to know that "one drive" has failed, you need to know which one, and which raid group its in.