is it true that you can still have your period if pregnant?

I've always heard that if you had your period not to worry because that means you're not pregnant. However I have also been hearing lately it is possible to still be pregnant and have a period every month? Is that true? I'm on the depo and I have my period every month since I've been on it (2 months) but lately I've been feeling sick very often and get heartburn all the time it drives me nuts. I wouldn't worry about it since I'm having normalish periods just longer but this whole period while pregnant thing now has me worried   My periods are two weeks long but they're like some days normal then other days light then they'll hardly drop so I think it's over gen start for another week. Then I'll get off my period for two weeks and start again with the same exactly thing