Looks like there might be a bug in CB Blogs not applying Itemid to its URLs properly. Have added a bug ticket to fix.
forge.joomlapolis.com/issues/9408
Additionally you do not have to use the Internal model with CB Blogs. You can set it to use Joomla and it will store blogs as Joomla articles allowing you to use all of Joomla's article display features on the blogs.