Generating a report that will show me any zero balance or unbilled invoices

Our scheduling software will generate a zero balance invoice when we do a job that will be billed after the job is complete because we do not know the time and materials that will be required for the job. I need to run a report that shows me unbilled/zero balance invoices. This is to double check that we are billing all jobs. I am able to generate a report that gives me zero balance invoices, but it includes the billed invoices that have been paid. How can I differentiate between them?