At a high level, the actual equipment you use doesn't matter, it's all
compatible. What really needs addressing is the configuration of that
equipment and the software to drive it. It's a pretty tall order and there
is risk here sharing files between two operating systems. You've got two
main concepts here: backup and file sharing.
A hardware free solution would be to give up on the local harddrive and
go with a solution like Ubuntu One, that gets the multi-OS sharing
requirement down, but not back up (yet anyways), it will sync all your files
Depending on how you execute your backup will directly impact how those
files are shared. For example, using something like duplicity on Linux,
all the files are compiled into archives and then expanded incrementally,
you can't browse the backups. You can restore from any point in time but
the trade off is you don't have immediate access to them. You need to settle
on what "backup" means to you and stick with that notion, if that means just
the latest copy of everything that matters to you mirrored somewhere else, then
things get a lot easier. However if you're considering backup in the traditional
sense, which is incremental, what you're asking for, to my knowledge, doesn't exist,
and would need to custom written.
Let's keep it simple for the sake of argument and suppose you want to do a straight
mirror of the files, like a snapshot, no incrementals. Now you still have the problem
of sharing files between to different operating systems. You have to compromise on
the filesystem here, like FAT32, so both Linux and Windows can have an easy time sharing volume. There are trade offs however, as FAT32 doesn't support UNIX symlinks.
Don't get fooled into using something like NTFS between the two, the Linux support has issues supporting WRITE and can corrupt the filesystem.
Once you've settled on the filesystem, you then need to really think about how the
automatic backups will function and what demands they'll make of the filesystem you
did choose. It may come to be that the software the WD comes with just doesn't work well with FAT32, in which case you'll need to search for a new solution. I would suggest searching for cross platform backup solutions first and then build out your configuration from there.
Finally, backup means backup, if you have a single disk, and it's not part of a redundant array, that disk goes bad and you've lost everything. Backup systems should really be atleast RAID1 with a hotspare on hand.
I give up on maintaining piles of HW after doing this for a better part of a decade and created a hybrid solution, using duplicity, an external disk and rsync.net, my backups are replicated to both. So if I have a problem, I can restore from the local external disk, which is fast, no network. If that drive fails too, I either replace it, or restore the computer directly. No local RAID array humming at home, no additional HW for care and feeding, I maintain only what I need, as I have better things to do.
Now what I just illustrated isn't a cross platform solution, which is even harder to pull off. There's a reason why these online cloud sharing solutions like U1 and dropbox are so popular, they just work. If you've got the time and inclination, you could probably create a custom solution too, but you also would need to understand how it works well enough to troubleshoot it. After all, what good is a backup if the system you deployed malfunctions, breaks down, and you lack the time/inclination/expertise to bring it online again?