In CORE, we have reimbursable expenses, which should not be confused with the billable expenses. There is a 'Reimbursable' check box in the Expense Items and Expense Entries screens that is different from the the client reimbursable expenses, called 'Billable'.
The Reimbursable and Billable flags are present in the Expense Items screen to set the default value of an expense. If you incur reimbursable expenses a lot, you should check the Reimbursable flag for all such expense items. Similarly, check the Billable flag to mark the expenses as billable by default.
The reimbursable expenses are to be reimbursed or paid back by the company to the employees, they might or not be billable to the clients. These count toward the A/P balance and are a liability. When you mark the employee expenses as reimbursable, they show up in the Bill Payments screen as a payable. This is handy especially if you run checks out of CORE. When you create new checks for employees, it tells you if there are reimbursable expenses associated and allows you to cut check for them. Even though you can use the same concept for vendor expenses, our recommendation is to create vendor bills instead for them. For vendor expenses that are related to projects, you can use the Items tab on the Vendor Bills screen. You can then write checks for them the same way.
On the other hand, the billable expenses are billed to the client and paid by the client to you. These count toward the A/R balance and are an asset.
When you incur expenses and plan to charge them to the clients as per the contract, they should be logged and marked as billable. These project-specific direct expenses should be logged against their respective projects and billed to the client. For your company's in-house and indirect expenses that are not project-specific, CORE can track them as overheads. It is recommended that you create an internal overhead project and track all your overhead expenses against it. Typically, these expenses are not billable nor reimbursable. There are many reports in CORE that show project-specific expenses and company overhead expenses.