Do you have any information about your father's death, such as where and an approximate date of his death, or your parents' marriage? Does your own birth record give your parents' places of birth? You didn't state a location of where these events took place (U.S., Canada, U.K., etc.). However, if in the U.S., generally, the more recent records of these types provide more information than older ones. These records could give you further clues to point you to new locations in which to search for more records that may provide you with more information about your family.
Hope this helps you.