The issue I'm experiencing is safari telling me that it can't open the page because it can't establish a secure connection to the server. Everyone else in my company is having the same issue. It's been like this ever since I installed the iOS9 beta and final release. I have an iPhone 6S running iOS 9.1. The web address I'm trying to access is http://mail.rathernotsaythenameofmycompany.com
Either provide the correct URL above by updating the thread of PM me, or use the Exchange Connectivity Analyser to find out what is going on. However, if it is affecting everyone in your company, it is likely to be infrastructure side rather than device side
I would bet a guess that the SSL Certificate isn't trusted by your (or anyone's) device. Maybe it's self generated and thus not trusted automatically by the phone... You could import the root certificate into the phone and see if that helps...
The problem is that iOS 9 dropped support for SSL3. That's the best your companies website will support. It's rather old and they should update to TLS. I'm not sure if it can be turned back on in iOS. ssllabs.com has some good tools that will let you see what ciphers and protocols your browser supports, as well as seeing that info for another website. You can go there and poke around if you want to learn a bit more about what is going on.