I want to connect to remote database using a program that is running in the local network behind the proxy. Is that possible?
You could also use RMI where your remote computer class that connects to the database acts as a remote server that talks RMI with the clients. if you implement this, then you will need to tunnel RMI through HTTP which is not that hard.
In summary, either have a servlet/JSP take HTTP requests, instantiate a class that handles database connections and send HTTP response back to the client or have the local class deployed as RMI server and send requests to it using RMI.