Using Pine bark and Cedar mulch together
Middlesex County New Jersey
One of the prime considerations when using mulch in the landscape is the overall purpose of the mulch. Most landscape plants would appreciate a shallow layer of mulch in summer to keep the soil cooler and about the same amount of mulch in the winter to keep the ground frozen, i.e., to prevent thawing and re-freezing of the soil which would result in soil heaving and root exposure.
Having said this, more than about two inches of mulch can suffocate shallow roots, i.e., deny much-needed oxygen which facilitates gaseous exchange in the plant's vascular system.
One drawback: the finer cedar mulch will probably settle into the larger lower layer of pine bark, allowing the larger bark particles to be caught up in the flow.
You may want to consider installing some sort of barrier system to break up the flow of water. Perhaps you could place some stones or landscape timbers in strategic locations to divert the water or to slow the flow. You could still use your choice of mulch between the barriers.