A compound-complex sentence contains coordinate and subordinate clauses:

When the door opened, a fox slipped through a hole in the floor and the chickens gave a cluck of relief.

The coordinate clauses are "a fox slipped through a hole in the floor" and "the chickens gave a cluck of relief".

The word 'and' is a coordinating conjunction.

The subordinate clause is "When the door opened".

The word 'when' is a subordinating conjunction.