Pointing to a externally hosted web page.

I recently started at a new company where the old IT named the AD domain company.com. My company does not host it’s websites internally, so on our internal DNS servers I have a record that points WWW to the external web host’s server. This needs to be done so people on our internal network can reach the companies web page. I was asked to deploy a blog page on the our website that is working for everyone put people on our network. The URL company web site is www.company.com but the only way to get the blog to work is to use the url of company.com/blog. Both the web page and the blog are hosted on the same server. What do I has to be done to allow internal people to access the blog?