As a reference, below is the snippet of code am using for demonstartion purpose, and rte is the object of type xamRichTextEditor control.

CharacterSettings cs = new CharacterSettings()
{
Bold = true,
Italics = true,
FontSize = new Extent(24, ExtentUnitType.Points),
FontSettings = new FontSettings() { Ascii = "Consolas" }
};
TextNode tn = new TextNode();
tn.Text = "Styled content";
RunNode rn = new RunNode();
rn.Settings = cs;
rn.ChildNodes.Add(tn);
ParagraphNode pn = new ParagraphNode();
pn.ChildNodes.Add(rn);
this.rte.Document.RootNode.Body.ChildNodes.Add(pn);

And when i copy the "Styled content"  text of the control, and paste into word, only the text is getting copied, the italic format is being lost.