half可以是名词，也可以是前位限定词，这里是作为前位限定词，用在中位限定词his之前。

the Englishman opposite him 写成 the opposite Englishman 也是可以的。

He drank off half his beer,still eyeing the Englishman opposite him.

为什么half his beer这个地方的half不需要加上of呢?  

the Englishman opposite him 写成 the opposite Englishman 可以吗?

    【答】《牛津英语用法指南》第四版478.1节指出：“half 或 half of 通常可用在与限定词（冠词、物主词或指示词）连用的名词前面。在这种情况下，half 之前通常不加 a 或 the 。 She spends half (of) her time travelling. 她把一半的时间用来旅行了。 (不能说： She spends a/the half ... ) I gave him half (of) a cheese pie to keep him quiet. 我给他半块奶酪饼，好让他安静下来。” 

     所以， half his beer  和 half of his beer 都是正确的。

     the Englishman opposite him 写成 the opposite Englishman 也是可以的,但是不能写成 the  opposite him Englishman。