Solid State Drives (SSDs) using flash memory storage technology present a promising storage solution for data-intensive applications due to their low latency, high bandwidth, and low power consumption compared to traditional hard disk drives. SSDs achieve these desirable characteristics using internal parallelism - parallel access to multiple internal flash memory chips - and a Flash Translation Layer (FTL) that determines where data is stored on those chips so that they do not wear out prematurely. Unfortunately, current state-of- the-art cache-based FTLs like the Demand-based Flash Translation Layer (DFTL) do not allow IO schedulers to take full advantage of internal parallelism because they impose a tight coupling between the logical-to-physical address translation and the data access. In this work, we propose an innovative IO scheduling policy called Parallel-DFTL that works with the DFTL to break the coupled address translation operations from data accesses. Parallel-DFTL schedules address translation and data access operations separately, allowing the SSD to use its flash access channel resources concurrently and fully for both types of operations. We present a performance model of FTL schemes that predicts the benefit of Parallel-DFTL against DFTL. We implemented our approach in an SSD simulator using real SSD device parameters, and used trace-driven simulation to evaluate its efficacy. Parallel-DFTL improved overall performance by up to 32% for the real IO workloads we tested, and up to two orders of magnitude for our synthetic test workloads. It is also found that Parallel-DFTL is able to achieve reasonable performance with a very small cache size.