I think Mint uses Ubuntu as its base rather than being part of the family. I couldn't see it now when I looked at downloads but Mint also used to offer a Debian (which I think Ubuntu uses as it's starting point) based version.

I'm not quite sure what you mean by "basic structure" but one thing that does vary is the layout of system files. I might for example find instructions for Ubuntu when looking for help (it's the most popular after all) and have to adapt them slightly for OpenSuse. Package management is another thing that varies. Ubuntu is deb based and Opensuse rpm based so instructions to apt-get won't work... It's easy usually though - the basic ideas remain the same.