I own and live in a duplex with 2 identical apartments. How much of my mortgage interest and property tax can I claim as a Itemized Deductions on Schedule A?

When you rent out part of your home, common expenses have to be apportioned between personal use and business use (rental) of your home. 

You need to calculate the percentage of business (rental) use. One common method is to divide the square footage of the rented portion by the total square footage of the house. In your case, this would be 50/50.

In the rental section, you will deduct as rental expenses the rental portion (total costs multiplied by the percentage of business use) of each common cost (such as mortgage interest, property taxes, utilities…). You also claim other costs specifically related to the rental such as repairs and maintenance, etc.

In the personal section, you will claim in Itemized deductions the personal use portion of mortgage interest and property taxes.

Please read this IRS publication, paragraph on Renting Part of Property on page 23.