Your relational design is fine, but what you are looking for is a Main-form sub-form setup.
Per your diagram: 1st Create an invoice form that contains just the information in your invoice table. I would use a combo box to populate the customerID from your customer table.
Next, create a second form for your line items table, and it should be set to display as "continuous forms" so that it will show multiple line items. Once again, use a combo box to enter productIDs from your Product table.
Finally, go back to your Invoice form and use the subform control to add the line item form to it, linking it with the InvoiceID field.
This is really a common setup, there are tons of examples. If you can get a copy of the venerable Northwind.mdb (tons of places it can be found on the internet), you can see how it is done.