Well, I have the same problem, I manage that like this.
Any billable task has a sub-task for the billing process and the person who complete the task assign the sub-task to the person in charge of billing. Then, when the person in charge make the invoice, put the number of the invoice in a "time slot" and complete the task.
That way, everyone knows the number of invoice for each task.
To separate the billable tasks from the normal tasks use a tag, that is the simplest way.
Hope it works for you.
Daniel..