[解決済み] 親コンテナを基準とした範囲の開始オフセットと終了オフセットを取得します。

function getSelectionCharacterOffsetWithin(element) {
    var start = 0;
    var end = 0;
    var doc = element.ownerDocument || element.document;
    var win = doc.defaultView || doc.parentWindow;
    var sel;
    if (typeof win.getSelection != "undefined") {
        sel = win.getSelection();
        if (sel.rangeCount > 0) {
            var range = win.getSelection().getRangeAt(0);
            var preCaretRange = range.cloneRange();
            preCaretRange.selectNodeContents(element);
            preCaretRange.setEnd(range.startContainer, range.startOffset);
            start = preCaretRange.toString().length;
            preCaretRange.setEnd(range.endContainer, range.endOffset);
            end = preCaretRange.toString().length;
        }
    } else if ( (sel = doc.selection) && sel.type != "Control") {
        var textRange = sel.createRange();
        var preCaretTextRange = doc.body.createTextRange();
        preCaretTextRange.moveToElementText(element);
        preCaretTextRange.setEndPoint("EndToStart", textRange);
        start = preCaretTextRange.text.length;
        preCaretTextRange.setEndPoint("EndToEnd", textRange);
        end = preCaretTextRange.text.length;
    }
    return { start: start, end: end };
}

function reportSelection() {
  var selOffsets = getSelectionCharacterOffsetWithin( document.getElementById("editor") );
  document.getElementById("selectionLog").innerHTML = "Selection offsets: " + selOffsets.start + ", " + selOffsets.end;
}

window.onload = function() {
  document.addEventListener("selectionchange", reportSelection, false);
  document.addEventListener("mouseup", reportSelection, false);
  document.addEventListener("mousedown", reportSelection, false);
  document.addEventListener("keyup", reportSelection, false);
};

#editor {
  padding: 5px;
  border: solid green 1px;
}

Select something in the content below:

<div id="editor" contenteditable="true">A <i>wombat</i> is a marsupial native to <b>Australia</b></div>
<div id="selectionLog"></div>