Our current system does not allow for true content access restriction at any role. The only real limit you can put in place is the ability to create or edit specific content types. Viewing published content is not a granular permission. There are some methods provided here, though, that will allow the ability to, for example, hide menus from a role. It doesn't restrict the content, it just restricts the path to the content.
You can create a menu and restrict the block to a particular role - this will at least hide the menu links from non-permitted roles. If someone with a non-permitted role were to get the url of a node within that block, though, the user would be able to view the content. To restrict a block based on a user's role, or restrict views output by role, please take a look at the related links provided.