This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Did you check out the Javadoc page of StyledDocument? I think not, or you would have found the getCharacterElement(int pos) method. That returns an Element that represent the single character. From the Element you can then retrieve the AttributeSet using getAttributes().