I actually did this for a work assignment of mine a few months back. I found out that Silverlight for WP7 did not allow me to have two MediaElements playing at the same time. What I did was create a Windows Phone Silverlight and XNA Application.
(Now Silverlight for WP7 finally created a background audio player so you can do it that way if you would like)
Your application can be entirely in Silverlight, but then you can use the XNA referenced (also you can have access to an update loop which is really nice)
XNA has a SoundEffect and SoundEffectInstance class
Then to load a sound just do the following:
Globals in you wrapper class Sound.cs
private SoundEffect Sound = null;
private SoundEffectInstance Instance = null;
Playing a Sound Effect in Sound.cs
Sound = ContentManager.Load<SoundEffect>(fileName); //ContentManager will have to be instantiated from wherever you create it.
Instance = Sound.CreateInstance();
Instance.Play();
Then just use the Silverlight MediaElement to play your video file.
XAML
<MediaElement x:Name="VideoPlayer" AutoPlay="False" Width="320" Height="220"/>
CodeBehind
VideoPlayer.Source = = new Uri("fileName", UriKind.Relative);
VideoPlayer.Play();
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