Reverse Proxy Solution to allow multiple virtual websites to exist under one domain

Description of support work: There are multiple websites (web assets) that are currently on different platforms (Linux/Apache & Windows/IIS). The also reside in one of two Content Management Systems (Umbraco [.Net] & Wordpress [Linux]). The job is to bring the assets together under a single domain structure, without having to port the websites themselves.

The solution calls for a Reverse Proxy and possibly some DNS forwarding.

ex. 2 websites
www.primary.com
blog.secondary.com

www.primary.com is served from IIS
blog.secondary.com is served from Apache

I want two things to happen:
1. www.primary.com\blog to pull up blog.secondary.com without changing the URL. www.primary.com\blog\post1 will pull up blog.secondary.com\post1, etc. All url in the client side html will reference www.primary.com\blog\... and not blog.secondary.com. The main concern is that the url does not change when going from primary to secondary and the website visitor is unaware that there are multiple sites being aggregated.

2. blog.secondary.com will either forward or perform a url rewrite to www.primary.com\blog. If we do not do this, it will be viewed by google as two copied websites and SEO value will suffer.

If there are other solutions to this problem - I will certainly entertain them. If I can get a system administrator with this expertise, there are many sites that need this architecture in place.
Extra notes: Like noted above, there are sites where www.primary.com is hosted on Linux/Apache, and others where it is hosted on Windows/IIS. blog.secondary.com is mainly hosted on Linux/Apache, but I would like a solution for Windows/IIS.