You can install 16.04 (or any other Ubuntu version) over your current installation. It won't interfere with your personal data. As long as you don't specify format the partition, it'll just delete system directories that your specified version uses.
It'll also inform you of this with this message:
The file system on /dev/sdXY assigned to / has not been marked for
formatting. Directories containing system files
(/etc,/lib,/usr,/var,...) that already exist under any defined
mountpoint will be deleted during the install.
Those directories will not have your data in them. Your home folder will not be touched. Also some local system areas such as
/opt will not be touched.
There's a chance that some of the configuration files in your
/home directory might cause some errors when you log in. You'll have to manually fix those. I usually do it by creating a new user when performing this type of install. Then I login between the two users, while I fix the applications or configurations that causes errors.