I read once (in this comment by Victor Mair on Language Log) that Chinese has single morphemes that span two hanzi. The example given was the Chinese word pútáo 葡萄. At the time, I assumed it applied to Japanese equally, because I assumed 葡萄{ぶどう} was the same word. I then assumed I could generalize from that to similar compounds. (In retrospect, I don't think that reasoning was very good, which is why I'm asking this question.)
Other compounds that look like they might be monomorphemic include [薔薇]{ばら}, [蜘蛛]{くも}, and 麒麟{きりん}.
Are any of these single morphemes? Pairs of bound morphemes? If these are bad examples, are there two-kanji compounds that are single morphemes?