Simple: You are looking for mhddfs.
It pretends to be one large filesystem, writes to the disks in the order they where mentioned and eventually moves large files to a different device, if the first one was too full. It can actually also use subfolders on the disks, allowing the same functionality.
The individual disks have to be mounted first and remain accessible. It does not alter the filesystems at all and does not care which filesystem is in place (as long as free space is correctly reported by the filesystem). In case a disk is lost, you'll have to remount your mhddfs again (on the fly) and the data on that disk is gone.
mhddfs /dir1,/dir2[,/path/to/dir3] /path/to/mount [-o options]
mhddfs#/path/to/dir1,/path/to/dir2 /mnt/point fuse defaults 0 0
Complex&Powerful: You want unionfs.
While mhddfs is nice and extremely simple, I've had problems with file permissions when granting others access via SSH. I couldn't find any solution, but found unionfs.
Unionfs also allows you to mount several folders across different filesystems into one, but does it's magic on permissions. You can merge several read only folders and one writable one together, so it appears as one. People you shared your merged folder with can then write to a read-only folder - as it appears to them - but the files end up in the single writable one. Linux boot CDs work like this, the writable disk is a ramdisk. People can even delete files in read only folders, which does not really delete the file, but creates a hidden whitelist file in their write-directory. If you catch all the options, you can basically use your filesystem as a poor mans SVN.
If you use the SVN-like options too much, you might miss data existing twice (improbable in your scenario, but possible), while your writable folder fills up with tiny, hidden whitelist-files. Other than that, it keeps your disks clean and individually usable. What happens if a file is too large for a disk, I don't know yet.
unionfs-fuse -o cow,max_files=32768 \
-o allow_other,use_ino,suid,dev,nonempty \
=rw makes the folder read and writable and
=ro makes it read only, even if the permissions would state otherwise. In
etc/fstab this is
unionfs-fuse#/path/to/dir1=rw:/path/to/dir2=ro:dir3 /path/to/mount fuse cow,allow_other 0 0