IE opens websites that FF and Safari don't...

Since IE is a Windows app, I figured this is the right place to post. If I was wrong, please redirect.

For work I am required to monitor some websites. A one in particular does open in IE, but it doesn't in Firefox or Safari. The only thing I've noticed is that the website is https and not http. I am not sure if this is the only difference. I've installed Parallels on my Macbook to use IE and to run a DOS program I need for work. But if I can find a solution to the browser issue and the DOS issue, then I can remove Windows from my Mac altogether.

Thanks in advance for any and all help.