PayPal standard does not have a a way to "push" the billing and separate shipping address.
Once the user is on the paypal site, they have the option to enter the Billing and Shipping details used for the transaction. These details for the order are available through your paypal account for lookup.
the normal workflow with paypal standard is to have a the customer enter their personal (doesn't necessarily mean billing address) information on the checkout page, when this posts to the confirm page the order summary and order details are stored in your database, in the orders table, there should be a status column that by default is set to pending.
the user then goes to the paypal site to select the payment method, enter the billing and shipping address.
When paypal accepts the payment method, the user is directed back to your site.
At this point, the transaction is in a queue to be processed with the merchant bank. In your paypal account you can set up to post the results of the transaction to an IPN page on your site, this IPN Post will contain the success or failure details of the transaction.
You will need to set up the IPN page to update the order status in the database.
If you dont use the IPN method, you can log into your paypal account to see orders that have been placed, view the status of the order, and the shipping address details.