It looks like your mhd files are associated with the installer executable instead of the Mids executable. You'll have to change that (it should be immediately available if you do a right-click + properties on a save file).
That was the first thing I thought of. It's not that. The MXD files are associated with the "Hero Designer.exe" file.
To add to the weirdness of this, this was all working fine not that long ago, and if I drag an MXD file on top of the Hero Designer.exe and release, it opens normally.
Edit: I seem to have it working now. I had to actually unassociate the files with Mids ("always open with: Wordpad"), then went into the list of registered file types, scrolled down the mxd, browsed back to the Mids executable, and made sure that "%1" was in the command string. That did the trick, although I couldn't see any actual change from what that was set to before. Oh well.