Pronoun

你的問題問得十分有意思：

首先講as...as...的結構

這種用法有以下的結構：

as + 形容詞／副詞 + as + 名詞／代名詞／從句，如：

She's as tall as her brother.
She speaks English as well as the rest of us.
It is as good as you expected.

或 as...as + 形容詞／副詞，如：

as soon as possible
as beautiful as ever

解釋了結構後，我們再看as後面的代詞
１）as 後面可以用賓語代詞（如：me, him等）在非正式文體這形式更為常見，如：

She sings as well as me.

但在嚴謹的文體中，as 後面多用主語＋動詞，如：
She sings as well as I do.

而你的句子，在現今的英語，則應寫為

You are not as handsome as he (is)

但在古舊的英語You are not as handsome as he其實也是正確，但現今這種用法已經十分罕見，不合潮流，故最好也是改為him，或he is


希望幫到你！