public class RichEditBoxExtended : RichEditBox
{
    public static readonly DependencyProperty RtfTextProperty =
        DependencyProperty.Register(
        "RtfText", typeof (string), typeof (RichEditBoxExtended),
        new PropertyMetadata(default(string), RtfTextPropertyChanged));

    private bool _lockChangeExecution;

    public RichEditBoxExtended()
    {
        TextChanged += RichEditBoxExtended_TextChanged;
    }

    public string RtfText
    {
        get { return (string) GetValue(RtfTextProperty); }
        set { SetValue(RtfTextProperty, value); }
    }

    private void RichEditBoxExtended_TextChanged(object sender, RoutedEventArgs e)
    {
        if (!_lockChangeExecution)
        {
            _lockChangeExecution = true;
            string text;
            Document.GetText(TextGetOptions.None, out text);
            if (string.IsNullOrWhiteSpace(text))
            {
                RtfText = "";
            }
            else
            {
                Document.GetText(TextGetOptions.FormatRtf, out text);
                RtfText = text;
            }
            _lockChangeExecution = false;
        }
    }

    private static void RtfTextPropertyChanged(DependencyObject dependencyObject,
        DependencyPropertyChangedEventArgs dependencyPropertyChangedEventArgs)
    {
        var rtb = dependencyObject as RichEditBoxExtended;
        if (rtb == null) return;
        if (!rtb._lockChangeExecution)
        {
            rtb._lockChangeExecution = true;
            rtb.Document.SetText(TextSetOptions.FormatRtf, rtb.RtfText);
            rtb._lockChangeExecution = false;
        }
    }
}