Not sure if this addresses your question exactly, but here's what I just figured out and it might help you also. I use Enterprise Suite, not Desktop, but I think these features would be the same across those platforms:
I found two options
Solution 1: For one specific payment, a Payment Receipt can be generated that shows the payment total a customer makes and also each invoice number, date and amount that was applied.
Pull up the Received Payment in Question [Customers>Transactions tab>select Received Payments>Double click on the payment in question. Once you see the "Customer Payment" titled screen with the date, amount and invoices checked that the payment is applied against [so that you know you are in the right place, this is the same screen we use to enter Received payments, so these fields are editable]>select Print at the yellow printer icon within the Receive Payments window>you can customize the print template if you want or hit "not now" button > click Preview to see what the print version would look like. It shows the amount customer paid and the invoice(s) and amounts that were applied to each invoice as well as the date it was applied.
Solution 2: For a report that shows many payments/many customers, go to Reports menu at top>Report Center> search bar within Report Center enter "CR610" (the report ID number of the "Payments Received" Report. The report search result looks like the screen shot included. Double click on this report and you can customize down to one Customer, if you wish. It will list each Payment Received and the Invoice numbers and amounts that were applied.
I hope this is helpful!
