Is it normal for my Windows 7 partition to be completely visible from Ubuntu? When In Windows 7 it cannot see any of the Linux partition, just its own partition.
I am a little worried something hasnt been set up correctly.
Yes, that is normal.
Ubuntu recognizes an incredible lot of filesystems and can read them (mostly write them too).
Windows recognizes only it's own FAT and NTFS, if we don't consider the filesystems of optical media.
That is the reason why Windows cannot read Ubuntu partitions, but that Ubuntu can read and write any Windows partition without any problem. There exist some projects like Ext2Fsd or zfs-win which bring partial support for some filesystems to Windows.
It is fine.
From Ubuntu you should be able to see your Windows partitions (if any).
From Windows, you are not able to view Linux partitions (