The source code shows the following:
FF3.6 ==>> <a href="http://example.com/seo_page.html">
IE8 ==>> <a href="/seo_page.html">
Google cache page viewed in FF3.6 ==>> <a href="/seo_page.html">
If you are saying that different browsers are showing you different "source code," then this means that your server is sending different code to different user-agents.
The <base href> value should be a full URL containing protocol, hostname, and URL-path, and this should NOT be changing based on the requesting user-agent. All user-agents should be receiving the same thing that you show for the Firefox case.