Might not be normal - none of my girlfriends ever mentionaed either the pain or the continued bleeding...
I know some hymen are tougher than others - some even have to be broken by a medic, but whether it is possible to only partially break the hymen during intercourse, I don't know, but if it is possible it certainly sounds like that could be the trouble...
I suggest more research and maybe a trip to see the medic or have a chat with the practice nurse or family planning clinic...