If you want to write it to the same drive/media you can do so; since it will be a separate backup job, it should not matter where you target the media. the separate db backup job should run fine and backup, and the big job should run fine as well. I would take out the db being backed up in the big job and just let it run in the separate job so that you do not get any errors.
This way you will have an organized backup; the database will be completely separate from everything else, which will save much confusion and the possibility of errors.
Hope that solved your question!
MD