1. it was at midnight后面加when引导
定语从句是可以的。
2. 但是由于前面it was的特点，在考试中一般（99.9%）来说，该句型一定还是个
强调句型，只不过后面的that...会加在when引导的定语从句的后面。如果前句有提示的话，甚至that...可以省略。
3. 如：
1）It was at midnight that the accident happened.
简单的强调句型，后面是that...。
2）It was at midnight (when I was sleeping at home) that the accident happened.
还原成正常句子：
The accident happened at midnight when I was sleeping at home.
即：被强调的时间状语中表时间的名词midnight另外又被when引导的定语从句所修饰。
3）对话：
---When did the accident happen?
---It was at midnight when I was sleeping at home (that the accident hapeen.)
即强调句型后面的that...，因为问句已经说出，在此处就可以省略。
注：这种情况相信楼主在做高三复习题时一定碰过（这种题目在我们这里还蛮流行的）。