。
She had the face of someone who'd been sick for a long time.
Literal
[topic-は] just-as long-time sick was-[as-if-such-as-かのような] face-look was.
まるで~かのような directly modifies 顔つき ('face-look'), giving 'a face-look as if [she had been sick for a long time].' 長い間 ('for a long time') uses 間 ('interval, duration') with the adjective 長い + the spatial/temporal の to form the noun phrase. The whole construction stacks: simile frame (まるで~かのような) → modifier of 顔つき → predicate であった (formal past copula). Three formal markers (である, であった, かのような) push the register decisively literary, the kind of narrative prose that suits novels and reflective essays.