Is there a common supertype (parent class) for a 'receipt' type (class) and an 'invoice' type (class)? It should be possible to state "an instance of receipt/invoice is a supertype."
I think the least ambiguous term that could encompass both an invoice and a reciept would be
bill. This is what I would recommend if you wanted an informal description. Some of the accounting and legal terms suggested by others might be better if your target audience is accountants and lawyers. If you're looking for a good class name that will mostly be consumed by programmers, then I would stick with "bill".
Source document is one term that's used in accounting: http://en.wikipedia.org/wiki/Category:Accounting_source_documents
The word voucher is used as an official legal/accounting translation of such an abstract term from Greek παραστατικό.
Merriam-Webster contains the following compatible definition 2.b: "a documentary record of a business transaction", as well as an incompatible definition 2.d: "a form or check indicating a credit against future purchases or expenditures" which semantically fits more with Wikipedia's definition: "A voucher is a bond which is worth a certain monetary value and which may be spent only for specific reasons or on specific goods."
However, under Accounts Payable, the Wikipedia article also gives the following definition: "A voucher is an accounting document representing an internal intent to make a payment to an external entity, such as a vendor or service provider."
When I take off my native English speaker hat and put on my software developer hat, it occurs to me that there is another way to answer this question - so I will add a separate answer to keep each point of view distinct.
In any accounts receivable / cash application app that I've ever worked on, it became abundantly obvious to me that there is not necessarily any strict correlation between what a customer is expected to pay (invoices) and what they actually pay at any given time (receipts). In many cases, these things don't even agree over time and you have to add adjustments (like credit notes or write-downs) to zero out a customer's account.
Therefore, instead of thinking about a word which has a meaning that can encompass both invoices and receipts, I think the best answer for Alexis' situation is to find a more broadly defined business object that includes both the expectation of payment and the payment actually received.
For this purpose, I would suggest the term: receivable.
Your invoices are statements of the expected amounts that are receivable and your receipts are statements of the actual amounts that are receivable. Maybe that is the best way to name your super-type?