Is It Normal To Have Periods While Pregnant?

Recently i discovered i was pregnant. I got my period jan 21. I missed my period feb 21 i took a test a day after and it was a faint positive. 3 days later i got a pregnant on clearblue 1-2 weeks it was digutal . Then today i started what seemed like my period but no clots with no cramping my mom says my grandma and herself had periods while pregnant is that normal?