As you can see on the page management, the Host pages are a seperate level.  If you want add there additional modules you can add them to the pages manually using the page management and add them for each page you want to have this module.

Basicly it is not wanted to add modules from several Portals using the inherit Methode.  If you have more then one Portal and you inherit modules from any of them you will have so many modules in the Host sites, that you don't need and you not real want to add to them.