Well, these are the basics ….

The ASIO driver is for direct access to the recording interface, completely bypassing the Windows sound subsystems.
The guarantees best stability, lowest latencies and lossless transport of audio.

The Windows sound subsystem is known to alter the sound and is not always working bit perfect. There are Windows drivers working bit perfect, but this is another story.

Windows and many applications like Firefox browser do not support the ASIO driver standard (which was developed by Steinberg a long time ago). They need a Windows compatible WDM driver.

For this purpose, you have to configure WDM devices in the RME driver settings. They are created dynamically.
Once you enable them, you see them appearing in the Windows Sound settings.

If I remember right for the Babyface Pro you can only enable WDM at once. For other recording interfaces (maybe also driver) this is different, there you can select WDM driver per I/O ports. If it is the latter it is recommended to enable them only for the I/O ports where Windows needs access to like e.g. ports to active monitors and headphones.

In the Windows sound settings you will see the icons of these dynamically created WDM drivers. With a right mouse click to the icon you can set either active monitors or headphones to the default Windows sound device.