Help on configuring multiple Virtual Hosts on the same servers using SSL certificates

I'm running into an issue trying to configure multiple applications on the same physical boxes to be accessed through an SSL connection (https) and could use some fairly detailed help on how to

The issue I am running into is this:

ApplicationA is a web application accessed through a Load Balanced address of https://mw-applicationa-lb.  The load balancer sends traffic to an IHS webserver running on either server1 or server2 (the app is horizontally clustered)  IHS, using the WAS plugin, redirects to the appropriate cluster in WebSphere Application Server (IHS, plugin and AppServer are all on the same server.. server1 and server2)

This basic configuration we have working...

The issue is when we add a 2nd application, ApplicationB in another cluster, responding to a different load balanced address, https://mw-applicationb-lb.

When a user tries to access the second application, they get a pop-up/warning that the certificate is invalid, because they are going to https://mw-applicationb-lb, but the certificate was issued to mw-applicationa-lb  We had thought we could add another certificate to the server for each virtual host, but it doesn't seem to be working.

I'm sure this is a fairly common configuration, but we haven't been able to get rid of this warning.  Anyone have thoughts on what we may be doing wrong?  I'm terribly inexperienced with SSL configurations, so please explain in some detail if you could.

If I need to provide more information, let me know

TIA,
 Brian