Beatrice was their real mother, in which she married Bertrand Baudelaire. They are the parents in which perished in the terrible fire which occured in the book 'The Bad Beginning'.
I'm sure you were a little confused as to if the story was true, or not. When I first completed reading the 'A Series Of Unfortunate Events', I truly believed that the tales written on their pages were real. Then, as I read the series a second time, I thought it was fiction - I didn't believe it - then, the third time I wasn't sure at all. So I looked up the life of Lemony Snicket and mostly everything in the book about the Baudelaire orphans are true. Mostly all the events which occur actually happened, although they are made to seem as though it is pure fiction.