Yes, it is doable.
You have to expose the box to the internet, with all the risks involved.
You have to make your modem/router redirect connections for your DDNS hostname to the box. You can do this in what is called "Demilitarized zone", where all services provided by the box are available to everybody out there, or only on a per-port/per-sevice basis.
You have to decide what service will be used to access the box: ftp? samba?
You have to decide if you will create accounts with a password for all your family users, or want them to access the box as the guest user.
Or you can use Google Picasa or Dropbox...