First, I cannot agree that there are two independent clauses here. There is one simple independent clause: "I will arrest him". There is a compound subordinate clause: "the man comes back and I am home". The coordinating conjunction "and" combines two complete clauses. The subordinating conjunction "if" relates the entire compound to the independent clause.
When a coordinating conjunction connects two independent clauses, a comma makes sense. In this case, the clauses are not independent.
When a sentence begins with a long introductory structure, a comma at the end of that structure makes sense. In this case, the compound subordinate clause is a long introductory structure.
Given these guidelines, it is appropriate to punctuate the sentence as follows:
If the man comes back and I am home, I will arrest him.
The reason that the "and" sounds natural is that it does connect two like things. Each of those things is a complete subordinate clause. The sentence also sounds natural if each of the subordinate clauses has its own subordinating conjunction:
If the man comes back and if I am at home, I will arrest him.
If the middle clause were independent, the meaning of the sentence would be completely different:
If the man comes back, I am at home, and I will arrest him.
