The first thing to do is make good backups of all personal files you want to save. do not bother with config files and applications, many will not cross distros safely.
Load Mint from the CD and start the installer.
At the partitioning page, take a look at the depiction of your hard drive at the top of the page and make note of the partition numbers for your Ubuntu partitions.
Choose "Specify Partitions Manually". Click forward to get to the manual partitioning page.
Find your Ubuntu partitions using the numbers you got from the previous page. Click on the / partition and click "Change" at the bottom of the partition table.
A window will open labeled "Edit Partition"
Do not change the size of the partition.
Change "Use as" from "Do not use this partition" to ext3 or ext4, whichever you prefer, using the drop down menu.
Check the "Format" box.
Mount point= /
Edit each Ubuntu partition the same way, choosing the correct Mount Point for each.
When all partitions have been edited, Click forward to continue the installation.
Reinstall the personal data you backed up earlier.
This procedure should work to install any distro using Ubiquity over any other distro. I use it constantly.