One way to punctuate a compound sentence correctly is to join the two independent clauses with

a comma.
a semicolon.
a comma and a subordinating conjunction.
a semicolon and a coordinating conjunction.

Your answer would be that you could bring together two independent clauses with a semicolon and with a coordinating conjunction.

Explanation:

A semicolon is generally used to link in a single sentence two independent clauses that are closely related in thought (1). When a semicolon is used to join two thoughts in a sentence, those ideas are given equal position or rank. However, you could also join these clauses by means of a coordinating conjunction, take 2.

1) Some people drink coca cola; others prefer pepsi

2) Mark is watching TV and his parents are making lunch

they fear for their lives