Hello ahagerman,
I checked and realized the report designer gives you the fields for Customer but it is not linked to the actual Invoice. I thought you could click, in the Field List and find it under the Invoice branch, but you can't. I'm not sure why it is like that in the Report Designer. What you can do is try adding the Balance field as a linked field in the Invoice table. (Customize -> Tables / Fields -> Invoice). It should now appear in the Invoice branch in the Field List.
Take a look at this screen shot. Here I am just about to add the Balance field from the Customer table to the Invoice table. I would recommend another name other than Balance. It's a very generic name.
Greg