I think Godless Dave put it as clearly and minimally as possible: congratulations!
Jabba, there will be 2 identical yous, each with an identical sense of self. But two, so if you die you are dead forever; but the duplicate will survive and will have no reason to think that they are not you. So you will die, but one of the two of you would live on. They would think that they were you, and they would have your body and continue your thoughts, continue your sense of self, unless by initial location or clothing after Xeroxing that they would know they were the copy.
If it helps, at least some of your molecules, and one of your physical DNA strands, may continue on in your children after you die, contributed by your sperm. Of course, apoptosis, necrosis and just wear and tear may have degraded and excreted those molecules, but there is some chance that one strand of DNA, out of the trillions that are in your child's body, came from you and is still there (recombined, etc, but still from part of you). Interestingly, there is evidence that some whole cells from the mom continue in the child's body for awhile, at least. So you and your wife may be immortal after all, in a very small way.