Typically if an invoice is due every month, there should be a recurring payment schedule which generates the invoice and marks it as paid when the payment comes in - the customer then gets the invoice already marked as paid.
If the customer is paying each invoice manually (which seems like an unnecessary burden on the client), nBill does not send a separate payment confirmation because the payment service provider would normally do this. For example, if they pay by Paypal, paypal sends a confirmation e-mail. Printable and e-mailable (if there is such a word) receipts are on the 'to do' list, but for now this task is deferred to the payment service provider.