In Drupal 6 all you had to do was copy a couple of files into your theme folder and ubercart would automatically recognize your customer invoice template.
Drupal 7 has a more difficult process where you would actually have to define your template file using a module. Fortunately, somebody came out with a module recently that automatically registers invoice template files in your theme.
Ubercart Register Invoice Templates module
Download and enable the module. Then proceed to the help page for instructions on how to set up your template file.
The nice thing about this in Drupal 7 is that you can have multiple templates rather than only being able to override the existing ones. This way you can setup different rules notifications which send different templates to whoever you want.