public class MyFolder
{
    public string Path { get; set; }
    public int Id { get; set; }
    public List<MyFile> FilesList { get; set; }
}

public class MyFile
{
    public string Path { get; set; }
    public int Size { get; set; }
}

public ObservableCollection<MyFolder> FoldersList { get; set; }

public MyFolder SelectedFolder
    {
        get { return selectedFolder; }
        set
        {
            selectedFolder = value;
            OnPropertyChanged(nameof(SelectedFolder));
        }
    }

<ListBox ItemsSource="{Binding Path=FoldersList.FilesList}"  SelectedItem="{Binding Path=SelectedFolder, Mode=OneWayToSource}">
    <ListBox.ItemTemplate>
        <DataTemplate>
            <StackPanel>
                <CheckBox IsChecked="{Binding ????}"/>
                <Label VerticalAlignment="Stretch" HorizontalAlignment="Stretch" Content="{Binding Path=Path}">
             </StackPanel>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>

<ListBox ItemsSource="{Binding Path=FoldersList.FilesList}"  SelectedItem="{Binding Path=SelectedFolder, Mode=OneWayToSource}">
   <ListBox.ItemTemplate>
       <DataTemplate>
          <StackPanel>
             <CheckBox IsChecked="{Binding Checked}"/>
             <Label VerticalAlignment="Stretch" HorizontalAlignment="Stretch" Content="{Binding Path=Path}">
          </StackPanel>
       </DataTemplate>
   </ListBox.ItemTemplate>
</ListBox>



public class MyFile : INotifyPropertyChanged
{
    public void SetPropertyChanged(string propertyName)
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }
    public event PropertyChangedEventHandler PropertyChanged;
    public string Path { get; set; }
    public int Size { get; set; }
    private bool _checked = false;
    public bool Checked
    {
        get {return _checked;}
        set
            {
               _checked = value;
               SetPropertyChanged("Checked");
    }
}