My site is available for brwsing on both HTTP-Port 80 and HTTPS-Port 443. Is there a way to prevent the browser pop-up window that alerts the user that their are secure and non-secure items on the site?

Yes, there's one way to do this: prevent the mixed content on your pages. This warning is there for a reason, and it warns the user that not everything is secured, even though they are going to a HTTPS:// website.