My father lost his job, and to make matters worse, my mother fell ill.
Literal
Father [subject-が] unemployment-did, furthermore bad thing [contrast-には], mother [subject-が] sick became-completely.
さらに悪いことには is a set phrase meaning 'to make matters worse / what's worse.' ~てしまった adds a sense of unfortunate, irreversible completion. A sentence about cascading misfortune.