Instructions at the Mininet website do not highlight that you have to add the host-only interface at the global preferences. You have to do this first and then configure it at a per-VM basis.
Once the global host-only interface is configured, head to the VM preferences and add an additional host-only interface. Now you will find the newly globally-added host-only interface as one of your options.
Getting inside the virtual machine from the host OS
Once the interfaces are all setup, you can start the Mininet VM.
The first thing you should do is tell Mininet about your new interface. After this, restart the VM and you can do ssh -Y mininet@<ip-of-the-host-only-interface>. It will prompt you for the VM passwork and then you are done, :).