This is how all of the Androids that I've ever used via HDMI work. When the device screen is off, the HDMI port is off as well. If you don't use HDMI, but instead output audio to the 3.5mm jack, or Bluetooth you won't have this issue. This is also how my Galaxy Nexus and Motorola Xoom behaved.
The Galaxy Nexus doesn't' have a HDMI port.