If you have a blog (hosted on typepad for example) and have the blog feeding into your web-site w/i a frame, does google & other web-sites count the blog as your web-site content?

a clear yes and no  
If you have hosted blog solution google and co will not count the content as something that belongs to your website. YET! the content you submit there will be ranked higher because the blogs you write on will usually have a kick a** pagerank which – if you place links back to your website – you/your website will benefit from. 
That being said: using a blog inside your website is interesting also. Reason being, that you provide your thoughts and insights on your corporate ID, etc. NOTE:! If you pull your feed into your website do not do it with frames because SEs will not index the content properly. Instead, use script to import the RSS feed, reformat it to fit your websites layout and then have it displayed there.