What is the complexity of determining Satisfiability of a CNF containing both Horn and Dual Horn clauses? 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?
3-CNF formulas contain a mixture of only Horn and dual-Horn clauses.  3-SAT, the Boolean satisfiability problem over 3-CNF formulas, is known to be NP-complete.  So it is unlikely that the satisfiability of such formulas can be decided in polynomial time.