Whenever a channel returns to the Wii Menu, it means that you don't have the proper IOSs installed to use said channel. The black screen error is unique to the HBC and IOS 60 do to the way the HBC installs via the new installation method. Regardless, your error is simply that you don't have the proper IOSs installed.
In other words:
Every now and then Nintendo updates their WAD format so that it won't boot into a channel unless a certain IOS is successfully detected. The WAD format the HBC uses must mirror one of the later Nintendo WAD formats and require a certain IOS to be present to boot. If you've only ever updated via a disc updates, I can personally guarantee you're missing said IOS needed to boot the channel.
So my advice to you is:
Since you have BootMii installed, make a NAND Backup. Then perform an online update via Nintendo and update to 4.1 Then the HBC should work. If not, reinstall via bannerbomb (but again, this shouldn't be necessary). If something goes horribly wrong, you have your NAND Backup to save you. However, there's no loss in homebrew functionality at all between 3.4 and 4.1 so you should be fine on both fronts.