How did you do this "mapping"? I'm not familiar with a way to map between fields. The way I do it is I use Insert > Quick Parts, and choose the SharePoint fields to insert them into my Word doc. Then, they are the same field, and there is no mapping. Whatever you put in that field in the Word doc reflects in SharePoint (and in the DIP), and it works in reverse. If you insert data into the DIP, it reflects in the Word doc. Even if you don't use the DIP, any metadata in the SharePoint item will show up in the Word doc (and vice versa) if you use Quick Parts.
THis particular feature isn't really related to InfoPath. Yes, the DIP is an InfoPath form, but it works nicely even if you don't touch InfoPath (it's built-in), and inserting SharePoint fields in the Word doc isn't affected by your DIP form. Is there something special you're doing with the DIP?