If you want them to always go back to the homepage on login then edit your CB Login module within Extensions > Modules then under Login Options set Login Redirect URL to index.php (no leading slash or anything). If you want them to return to their previous location where they attempted to login (if possible) then leave blank. If you want to go to a specific page be sure to always provide the non-SEF URL beginning within index.php.

Joomla won't allow you to set 2 menu items to home even if they've different ACL. So having 2 different homepages can be a bit tricky and takes workarounds like using modules or content articles for different homepages based off ACL.

If your homepage is just a Joomla article for example then create a new Joomla content category and call it "Home" for example. Now create 1 article with access set to Guest and another set to Registered. Next set your home URL to display the articles from the "Home" category and it'll display the respective article based off the users access.

Believe there's also extensions that'll let you do this as it'd be a simple system plugin that just acts on the routing or after rendering to redirect to a different home URL.

For further suggestions I recommend posting to the Joomla.org forums though as this isn't something CB has any control over or can do anything about.