Actually, women who are pregnant cannot have true menstraul periods. The uterine lining thickens and does not shed during pregnancy; this lining is what is lost during menstruation.
Some women do experience light spotting for various reasons - implantation, cervix gets bumped, etcetera - and mistake this bleeding for a period, especially if they are looking for physical signs that they are or are not pregnant. However, this bleeding rarely occurs every month, and women who go their entire pregnancies without noticing are usually those who have a past of irregular menstrual cycle. Women who think they are postmenopausal or are going through menopause can also get pregnant without realizing. And, sad as it seems, there are cases where the woman is just in total denial and convices herself that there is no possible way she could be pregnant. This was the case with a friend of mine from highschool.
So, in general, if your periods are just as heavy as they normally are, don't fret. Home pregnancy tests can also alleviate any leftover nervousness. Be sure you're using your chosen form of birthcontrol correctly every time, and you shouldn't have anything to worry about.