Deep neural networks (DNN) use a wide range of network topologies to achieve high accuracy within diverse applications. This model diversity makes it impossible to identify a single "dataflow" (execution schedule) to perform optimally across all possible layers and network topologies. Several frameworks support the exploration of the best dataflow for a given DNN layer and hardware. However, switching the dataflow from one layer to the next layer within one DNN model can result in hardware inefficiencies stemming from memory data layout mismatch among the layers. Unfortunately, all existing frameworks treat each layer independently and typically model memories as black boxes (one large monolithic wide memory), which ignores the data layout and can not deal with the data layout dependencies of sequential layers. These frameworks are not capable of doing dataflow cross-layer optimization. This work, hence, aims at cross-layer dataflow optimization, taking the data dependency and data layout reshuffling overheads among layers into account. Additionally, we propose to exploit the multibank memories typically present in modern DNN accelerators towards efficiently reshuffling data to support more dataflow at low overhead. These innovations are supported through the Cross-layer Memory-aware Dataflow Scheduler (CMDS). CMDS can model DNN execution energy/latency while considering the different data layout requirements due to the varied optimal dataflow of layers. Compared with the state-of-the-art (SOTA), which performs layer-optimized memory-unaware scheduling, CMDS achieves up to 5.5X energy reduction and 1.35X latency reduction with negligible hardware cost.