One Site/Blog, Different themes

Is it possible for me, with a free or paid theme, use one theme on the front page of your WordPress site or on separate pages and another on another without using sub-domains? Do I need to set some settings or change settings? I want my blog to be a site and a blog too, under the same installation. I want a blog and a site in one, with the blog part using quick and smart interactions with comments etc and the site being more vast and professional. Perhaps with a one page theme on the front page and another theme for blogs.

Be specific.

Can anyone help me out?