In Zoho Invoice, you can record expenses either as 'Billable' or 'Non-Billable'. To get reimbursement for an expense, you need to link a customer to the particular expense. You can record a billable expense which can be converted into an invoice later. Getting a payment for the invoice will reimburse the expense.
All you need to do is to tick the check-mark on the "Billable Expense" field in the "Record Expense" page. This will allow you to select the customer. Later the expense can be converted into an invoice and reimbursed..
Zoho Invoice FAQ