You can't reference a resource dictionary contained in a Window-type XAML file, from another file. What you need to do is create a separate resource dictionary, "Shared.xaml" or whatever:
<ResourceDictionary ... >
<Style TargetType="{x:Type s:SurfaceListBox}" x:Key="FatherStyle" >
</ResourceDictionary>
Now reference the shared one from your main window:
... and also from "MyResourceDictionary.xaml":
<ResourceDictionary xmlns="........."
and so on >
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="Shared.xaml" />
</ResourceDictionary.MergedDictionaries>
<Style TargetType="{x:Type s:SurfaceListBox}" x:Key="ChildStyle" BasedOn="{StaticResource FatherStyle}" />
</ResourceDictionary>
And now in your "MyUI.xaml" window, you should be able to access the "ChildStyle" as you expected, by referencing "MyResourceDictionary":
<ResourceDictionary xmlns="........."
and so on >
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="MyResourceDictionary.xaml" />
</ResourceDictionary.MergedDictionaries>
<s:SurfaceListBox Style="{StaticResource ResourceKey=ChildStyle}" />
</ResourceDictionary>