the black membrane is the underfelt. water shouldnt reach this unless a tile has come loose or broke. get a competent roofer to check for you. an emergency measure would be to use flashing tape
( bought from most big diy shops ) to cover the tears. They are bitumen backed so once applied they need heating up slightly to soften the bitumen and provide a water tight seal. If you not got a gas gun then use a hairdryer.
Gary
May 2006