Client certificate required after installing certificate
You are looking for a client certificate.  It would seem if you are trying to obtain it from the URL that you are actually getting the server certificate to place in your keychain.

Normally a client certificate is a certificate that identifies the user, or at times the machine, that the request is coming from (ie. not the server you are accessing via Safari).

A client certificate would normally reside in your Login keychain and not the system keychain as it identifies you.

The client certificate is normally provided from the server by some other means rather than accessing the browser, as that is an insecure delivery method.

You need to talk to the owner of the internal server and ask them to provide a client certificate, or if two-way certificate identification is not required then have it turned off in the internal server instead.