My husband set the table and washed the dishes
NOT A TEACHER
(1) It might be helpful if you remembered the definition of a compound sentence:
Two independent sentences connected by a conjunction.
For example:
Otevia lives in Nigeria, and she studies English.
If I were to delete (erase) the conjunction, we would have two independent sentences:
Otevia lives in Nigeria.
She studies English.
(2) Thus, you can see that your sentence is not a compound sentence.
(3) Your sentence could be written like this:
My husband set the table, and my husband washed the dishes.
Now, that is a compound sentence! But it sounds funny. So native speakers
prefer to say: My husband set the table and washed the dishes.
As you know, the grammar books call the words in bold a "compound predicate."
P.S. You are 100% correct: your sentence is a simple sentence with a compound predicate.