Between the two periods of classes is a break,---we can have

这是一个非限制性定语从句,要用关系副词when来引导.
这个句子中,Between the two periods of classes is a break和we can have a short rest 是从属关系,后面的句子是用来修饰break的.这个句子主要的意思是在前面,在两堂课之前是课间休息.后面的从句（我们可以有短暂的休息）是对break的进一步说明.
then是一个连词,它连接的两个句子是并列关系,如：
We finished the first class,then we had a short rest.