I've heard from numerous sources that the pill takes a full two months to become completely effective, so you should still be using another form of protection on top of the pill for the next few months. To answer your original question - the pill doesn't "stop" working during the week of her period, so once it's been a few months you can have sex during her period with the same amount of protection as any other time in her cycle.
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"The world is so exquisite with so much love and moral depth, that there is no reason to deceive ourselves with pretty stories for which there’s little good evidence. Far better it seems to me, in our vulnerability, is to look death in the eye and to be grateful every day for the brief but magnificent opportunity that life provides"
-Carl Sagan
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