Embodiments herein describe a 3D flash memory system that includes multiple blocks where each block contains multiple pages arranged in a vertical stack. Instead of having a single command line indicating whether a read or program is to be performed, separate command lines are coupled to each of the blocks. As a result, if the memory system identifies a read request and a program request to different blocks, the requests can be performed in parallel. In one embodiment, a program command line is used to perform a program request on a first block while a read command line is used to perform a read request on a second block in the 3D flash memory system in parallel. Furthermore, because a program request can take much longer to complete than a read request, the 3D flash memory system can perform multiple read requests in parallel with the program request.