if a third party wants to contribute its product to NHibernateContrib, then the integration code would offcourse be open source. But, if it is required that the product itself be the open source?

A contribution can be added to NHibernateContrib with the integration code under the LGPL; and your assemblies (+ license) will stay in /lib/ directory (like Bamboo.Prevalence)

You can also make it available somewhere (on your website for example) then make a post here to describe it :)
A good thing would be to write a documentation (as an article/quickstart) ;)

Read How to contribute to NHibernateContrib.

I don't think your product has to be open-source if you want to integrate it with NHibernate. But is there any point in adding the integration code to NHC when you can just make it available for the users to download together with your product?