Prevailing LLM serving engines employ expert parallelism (EP) to implement multi-device inference of massive MoE models. However, the efficiency of expert parallel inference is largely bounded by inter-device communication, as EP embraces expensive all-to-all collectives to route tokens to the remote experts if not collocating on the same GPU/NPU device. Nevertheless, state-of-the-art schemes treat expert device-placement and request (or token) device-scheduling as separate concerns, triggering excessive communication between them and compromising inference efficiency This paper proposes Semantic Parallelism, a novel parallelism paradigm that minimizes the steep communication costs in EP-centric MoE serving via model-data collaborative scheduling. We implement Semantic Parallelism in a framework called Sem-MoE. Sem-MoE maximally collocates experts and their activating tokens onto the same device using proactively modeled activation likelihood between them and introduces three key techniques: (1) Offline model scheduling, which preliminarily clusters and collocates experts onto devices based on their co-activation tendencies for certain classes of input. (2) Online inter-request data scheduling for Attention-DP setups, which proactively rebatches incoming requests onto the device that hosts experts most likely and frequently activated by the corresponding requests. (3) Online intra-request data scheduling for Attention-TP setups, which seamlessly fuses a token reshuffling procedure into the original inference pipeline and proactively reschedules tokens to devices to reduce dispersed remote routing. We build Sem-MoE into a prevailing LLM serving engine SGLANG. Experiments show our collaborative scheduling approach can effectively reduce the all-to-all communication volume in EP and achieve superior inference throughput compared to existing solutions.