Believe it or not, the answer is "yes". As long as you don't mind the mess, sex during menstruation is safe. Let me rectify that: about as safe as it can be expected. Blood is a medium in which certain infectious agents multiply, so you might want to consider that before starting. Also, the chance of getting HIV is probably sky-high with all that blood around. Better use a condom if you are not sure of yourself or your partner. Still, there is no medical reason why a mutually monogamous couple (which is also free of STDs) should not have sex during menses.
But if you are not scared by these problems, then you can go right ahead. Of course you should wait for your lady to get over the worst days of her period, if you want sex to be any fun that is. The best idea is to spread a towel on the bed in order to keep the blood off the sheets, preferably a black or dark red towel. You can try any position you want, but your best bet is to stay on top and have the lady below. This should limit the flow of blood a little. The lady could also put to good use a diaphragm or a menstrual cup in order to keep the blood in, at least for a while.
The biggest risks brought by sex during menstruation are an increase in the risk of pelvic infections and HIV (because the opening of the cervix widens) and also a higher risk of pregnancy. Yep, you read that right: pregnancy. Just because your lady is having her period does not mean that you cannot get her pregnant. It's rare, I'll grant you that, but it did happen quite a few times.