While the mood is dark, Gaiman balances it with light, just as the illustrations do too. The woodcutter father loves his children and truly regrets leaving them in the woods. He's just a dolt that can't come up with another solution. The mother is more grim (or Grimm) for she clearly wants to save only herself and initially tells the father to "kill them." The father refuses to do a monstrous act like that and instead agrees to "lose" the children in the forest.
The son overhears this conversation and leaves rocks to find his way home with his sister. They return to an overjoyed father who takes them out to the forest to die again. The second time they leave, Hansel only has time to get bread and the birds eat it making it impossible for them to get home. Hansel is clever and while his sister does not seem so at first, she is the one that outwits the old witchy woman. She pushes her into the fire by pretending to be dumb and not know how to cook.
The sparse writing reminds me of some of the original fairy tales I have read that were written for adults, but Gaiman makes it his own giving it a modern flavor. The Author's notes explain how the fairy tale has changed over the years and should not be missed. Those that are purists to the tale they grew up with and want it to read like that might be disappointed on this take. Personally, I ate it up once and read it again for dessert. Truly delicious.