What is the complexity of determining Satisfiability of a CNF containing both Horn and Dual Horn clauses?

Question

If a CNF contains both horn and dual horn clauses and does not contain clauses of other types, then can its Satisfiability always be determined in polynomial time?

If the answer to the above problem is yes, then suppose we only add XOR clauses in addition to horn and dual horn clauses, can the Satisfiability of this type of CNF be determined in polynomial time?