Thanks everyone for your responses. I can see that it is best to simply use www.blockandcompany.com/blog versus www.blog.blockandcompany.com.
In checking again with the company that runs my site, I was told there are problems running a site based on Coldfusion (which my site runs) and Wordpress (with is PHP based). I guess they don't play well in the same environment so that is why they are recommending hosting the blog on a different server and using a subdomain. Looks like I'm stuck doing it this way.