Properly securing a web server with possible access to medical information requires multiple layers of security, strong authentication, and encryption.
Adding a web server to your mail server is going to expose you to vulnerabilities at the network layer, the OS layer, and the application layer. Detecting these vulnerabilties and implementing the appropriate security controls is no trivial matter.
I've seen many servers totally 'owned' by some obscure SSL vulnerability or one small firewall rule mistake. And once your mail server is owned, that would be launching point into your database servers, your application servers, etc.
Please, please familiarize yourself with HIPAA regulations and do not try to host this web site yourself.
The safest way to do this might be to mirror your intranet to a third-party service provider.
Alternately, you could deploy a SSL VPN solution from Cisco, Juniper, WatchGuard, or other vendors. By establishing an encrypted SSL connection thru a VPN solution, you could deploy strong authentication and allow access to content in a secure fashion without exposing your network, server, or data to attack.