Work from the bottom up when setting mixed permissions at the folder level.
Start with everything in the Sandbox hidden for a role and then un-hide folders to give access.

Please note permissions cannot be set at the file level in the Sandbox.

1. Select a role on the right.
2. Click the green Edit button.
3. Click the dot under Hidden next to the segmented permissions bar that lines up with the Staging Folder. This will turn the dot red and hide the entire contents of the Sandbox for this role.
4. Click the arrow to the left of the Staging Folder in the navigation pane on the left to expand it down, so all folders are visible.
   Also, do this for any nested folders where you need to set access permissions.
5. Click the fourth segment of the segmented bar next to a folder to grant Manage access to the role.
   You won't be able to select View, Print, or Download for any folders. 
   The Staging Folder and any sub parent folder are systematically changed from Hidden to View access so the role can navigate.
6. Click Save.