Employee reimbursement through payroll, but costs must be allocated to a project.

Let me preface this by saying I am very new to QBO and just started using the system. 

We track 95% of our costs to customers/projects and try to reimburse employees for company related purchases, mileage (non-taxable) reimbursement, and living out allowance/per diem (non-taxable) on their pay cheques. 

I understand how to reimburse an employee in QBO payroll and have set up my reimbursement descriptions but I haven't found a way to record the expenses to the projects correctly and reflect the payment in payroll.  Is there a way to enter the expense to allocate the cost to the correct project and account/category while still reimbursing the employee on their payroll cheque or if I want to track the costs to a project is the only solution to issue a separate cheque?  

Thanks in advance for your thoughts, suggestions, and assistance.