High-throughput inference serving is essential for applications built on large language models (LLMs). Existing serving frameworks reduce request-level and batch-level bubbles through batching and scheduling, but often overlook bubbles within each decode iteration. Tokens generated in the same iteration may incur different costs because they depend on KV caches of different lengths; tokens with long KV caches can become bottlenecks and delay the next iteration. We propose AlignedServe, an LLM serving framework built around prefix-aware batching. It groups requests with similar KV-cache lengths into the same batch to reduce iteration-level bubbles. To support this policy efficiently, AlignedServe uses large CPU memory to maintain sufficient in-flight requests for batching and applies a batch-level scheduling policy to reduce batch-level bubbles. It also introduces a GPU-Prefetch-For-GPU architecture, where one GPU prefetches KV cache for another to reduce CPU-to-GPU transfer latency. Experiments on synthetic and application workloads show that AlignedServe improves decoding throughput by up to 1.98 times and reduces latency by up to 7.4 times over state-of-the-art systems.