What I see is a classic case of where the scene's dynamic range exceeds the sensor's dynamic range, and there is no magical auto mode that will correct it. No matter how sophisticated a camera's matrix metering system is (and yes, your camera was set to Matrix Metering), in some situations like this there is nothing that the camera by itself could have done better. To have a well-balanced exposure in a scene such as this requires some input from the user. This "input" is something that you will learn over time and by asking questions, like you are here. What I would have done differently if I wanted both the background and foreground properly exposed:
1. Lower the ISO. Lower ISO's maximize the camera sensor's dynamic range. A setting of ISO 160 would still yield a sufficiently fast shutter speed to hand-hold and given the static nature of the subjects, been more than fast enough to stop any subject motion.
2. Zoom in on the background and press the AE lock button to set proper exposure on the background (or you could set the exposure mode to manual, and set the exposure yourself based upon the reading while zoomed in on the background).
3. Zoom back out, recompose, focus and use flash to fill-in the subjects. The i-TTL feature of the flash will automatically balance the foreground since it is linked to the focus point(s).
I also noticed in the exif data that the camera was set to manual white balance. Since white balance can effect exposure, if not using auto white balance, make sure that your manual white balance setting is appropriate for the scene. Additionally, your Picture Control settings were +1 on contrast, thereby compounding an already high contrast scene. When shooting with a DSLR it is important to expose for the highlights and you can enhance shadow detail in post-processing (if needed). Blown-out highlights are unrecoverable (with any texture/detail/saturation) in a DSLR. Active D-Lighting may help in scenes such as this.
Hope some of this helps. Keep shooting, experimenting, asking questions and soon enough tricky lighting situations like this will easily be overcome.