Por favor, intente esto, espero que ayude.
DELETE FROM departure, departure_time
USING departure
INNER JOIN departure_time
WHERE departure_date = '2016-09-30'
AND departure_time.id = departure.id
O
DELETE FROM departure, departure_time
USING departure
INNER JOIN departure_time
WHERE departure_date = '2016-09-30'
AND departure_time.departure_id = departure.id
O puede usar ON DELETE CASCADE
eso funcionará automáticamente para usted.