While logically it seems to be a reimbursement, it is not, it is income and posts to its own income account if you want, but income and expense are never posted in the same account - not sure if the last comment applies I wasn't real sure if that was your intent or not.
You don't say but I will assume you are using QBO
If you have QBO PLus, In company settings turn on make expenses and items billable
check mark to track billable expenses and items as income
then in company settings>advanced>chart of accounts click the edit pencil and select the billable expense income account
Why intuit separated the two related settings is anyone's guess
When you enter a vendor bill/CC charge/etc, you will see a Billable check mark box, check that and select the customer name in the customer block. The next time you invoice your customer, the system will show billable expenses on the right side that you can click the add link to add the bill to the invoice. IF you do not want to add the bill to the invoice, leave the billable check mark box blank, the cost of the expense will still count against the customer
Then, on the invoice, add your service item which would point to its own income account.