Journal Entry

@MMK48 

QB Desktop will not allow you to do a journal entry with A/R and A/P on the same journal entry which is what you need to do in this case.  

The best way to do this is to create a bank account in QB called 'Clearing Account' and use that to offset the invoice and bill.  Receive payment on the customer's invoice and deposit it to the newly-created bank Clearing Account.  Then, pay down the bill by the same amount using the same Clearing Account.  You now have the invoice paid and a balance remaining on the bill that you can pay.  This works if the bill amount exceeds the invoice.  If the invoice amount exceeds the bill, reverse the process - pay the bill and then receive payment on invoice.

@MMK48 

"Would they allow me to add another line in the same Journal Entry and somehow get it into the vendors account?"

Nope.  You can make two journal entries:

#1 - Debit A/P (list vendor), credit Clearing Account

#2 - Debit Clearing Account, credit A/R (list customer)

But, then you need to apply those credits to the invoice and bill.  The instructions in my first do the same thing but in fewer steps.