Not sure an integration is wished neither by brian binnerup opening up his database nor by the JRiver team. Both softwares do not cover the same thing. while MC river is geared towards quality playback with customizable dsp's for audio and madvr (video), Mymovies is a video library manager which adds on top of windows media center.
MC also has a good tagging utility which is less detailed than my movies but works OK. Also JRiver takes its info from publicly available databases whilst Mymovies after retrieving stores your personal collection info.
If you want to use Mymovies tags you can set (requires an amount of points) metatags in Mymovies to be stored in JRiver sidecar format. JRiver can then use these tags directly.
