As you are using your car for your job - you may deduct your car expenses.
Generally - you have a choice - to deduct either actual car expenses or claim a deduction based on mileage. But you may not use both methods at the same time.
Because part of your expenses are reimbursed by your employer - that amount should be subtracted from your travel expenses (regardless which deduction method you are using.
Please use IRS publication 463 for reference - http://www.irs.gov/pub/irs-pdf/p463.pdf
If you lease a car, truck, or van that you use in your business, you can use the standard mileage rate or actual expenses to figure your deductible expense.
If you choose to use actual expenses, you can deduct the part of each lease payment that is for the use of the car in your business. You cannot deduct any part of a lease payment that is for personal use of the car, such as commuting.
If you lease a car that you use in your business for a lease term of 30 days or more, you may have to include an inclusion amount in your income for each tax year you lease the car. To do this, you do not add an amount to income. Instead, you reduce your deduction for your lease payment. (This reduction has an effect similar to the limit on the depreciation deduction you would have on the car if you owned it.)
Let me know if you need any help.