Hereditary Menstrual bleeding during pregnancy?

No, it's definitely possible but it's not menstrual bleeding because you can't get a 'period' while you're pregnant (it's just known as l bleeding). In fact, lots of women have l bleeding during their pregnancies. Some women may have it throughout their entire pregnancies and others might just have it in the beginning. I'm sure it could possibly be hereditary too, but that's something you'd either have to ask your doctor or wait until you're pregnant yourself to find out.