You do not have reimbursed expenses, only employees do

You have expenses, you may or may not invoice the client for them and may or may not mark them up, in any case they  pay the invoice and that is your income

On the P&L your expenses reduce gross income to get net taxable income

Yes you can post what you are calling reimbursable expense to one general expense account account, if you wish.  And the income to another income account.  You do not net income and expense in one account.