Billable Expenses for Project cause Incorrect reporting of Income and Expense in Profit and Loss report

Billable Expenses for Project cause Incorrect reporting of Income and Expense in Profit and Loss report

The "billable expense" function breaks the Profit and Loss reporting for project expenses that should be reported as both income and expenses.

The example: A matching grant reimburses a percent of specific expenses for a project, but it is not considered "pass through" reimbursement, and must be included in gross income.

The customer (in Books) is "Granting Agency", and "Grant Project" is in Zoho Projects.

Using example amounts, there is a "Rent Expense" of USD$100, and 50% reimbursement rate.

What is expected on profit and Loss statement
Operating Income:
      General Income: $50
Expense:
      Rent Expense: $100

What actually appears on P&L is:
Operating Income:
      Discount: -$50
Expense:
      Rent Expense: $0

How is this reproduced?
The Rent Expense is paid via credit card.

In the credit card screen, editing the transaction to change customer to "Granting Agency", Project to "Grant Project", and flagging the expense as "Billable" works to bring it to the Invoice screen.

Entering a new invoice, and selecting the unbilled expense works to create an invoice and link the expense.
A discount amount is added (it works the same whether via line item discount or "adjustment" to the total), and the net invoice is $50

The invoice is later paid and deposited to a checking account.  All of the steps appear to correctly match:
billable expense --> invoice --> payment --> deposit

The discrepancy is visible in the Chart of Accounts:
Rent Expense shows a $100 Debit for the Expense and a $100 Credit for the Invoice = net $0
The Income:Discount account shows a -$50 Debit on the invoice.

Although the net income is correct, the Income/Expense components are incorrect and unmatched - the "discount" is not appropriate to show as negative income, and the rent expense should not be zero.  "Billable Expenses" appear to only process as "pass through" transactions that are not intended to show up on P&L or perhaps other financial reports (I haven't reviewed the details how it affects Cash Flow, Balance Sheet, or other reports).

Currently, it appears the workaround is to NOT use billable expenses. If I make expenses non-billable, and then create an invoice for a new "Item" "Grant Reimbursement" (created as a non-taxable service), then the reimbursement shows up as income, and the expense shows as an expense. However, with this workaround, there is not a link between the expense and reimbursement.

Is there a setting or something to make billable expenses show up in both gross income and as an expense?