For QB desktop:

This worked for me:

Create a Reimbursement Account (Other Current Liability). Enter the vendor bill normally (use normal account, amount, customer: job, class). Go to Pay Bills, select the bill in question and click Discount Info. and enter the amount of the vendor bill as a discount and use the Reimbursement Account (the one you created in first step)  - this "pays" the bill" to the vendor. Issue a check to the employee ( or whoever paid the invoice) and use the Reimbursement Account as the account. This pulls the expense through. This process generates a journal entry in Accounts Payable for the Vendor (increase) which is offset by the payment to the employee for the equal amount paid to the vendor (decrease). The net effect is that the Reimbursement account has a zero balance. The expense is shown in P&L associated with the Vendor.