在这里Jenny told him she wanted to go home是主句,而As soon as he had finished是一个状语从句.
下面是as soon as的用法用作参考：
它的意思相当于“A事情发生以后,就做B这件事”.
这个短语用的比较常用,口语和书面语都可以.它的特点是,在句子中的位置比较灵活,而且可以用于各种时态.例如：
I’ll write you as soon as I get there.
我一到那儿就给你来信.（一般现在时）
As soon as I went in,Katherine cried out with pleasure.
我一进门,Katherine 就高兴的叫起来.（一般过去时）
I’ll return the book as soon as I have read it.
我一读完就把书还回去.（现在完成时）
Andrew left as soon as he had drunk his coffee.
Andrew一喝完咖啡就走了.（过去完成时）