Visual document understanding typically requires separate retrieval and generation models, doubling memory and system complexity. We present Hydra, a dual-head approach that provides both ColBERT-style late-interaction retrieval and autoregressive generation from a single vision-language model. A single LoRA adapter, trained only for retrieval, is toggled at inference: enabling it produces multi-vector embeddings; disabling it recovers the base model's generation quality, with 426 of 426 language-model weight tensors byte-for-byte identical to a freshly-loaded Qwen3.5-4B. We identify two failure modes that can silently break generation in retrieval-fine-tuned VLMs (attention-mode restoration and lm_head preservation) plus an efficiency requirement (KV-cache-aware decoding); Hydra sidesteps the first two structurally and addresses the third in the decode loop. We release two scales, Hydra-4B and Hydra-0.8B, sharing LoRA hyperparameters (r=32, alpha=32) and optimisation recipe; data mix and projection dim differ across scales. The single-model design cuts peak GPU memory from 28.85 GB to 10.77 GB at 4B (62.7% reduction) and from 5.79 GB to 2.37 GB at 0.8B (59.1%) relative to a co-resident two-model deployment. A controlled ablation finds GritLM-style joint training matches Hydra's retrieval-only training on the evaluated modes while its LoRA-on generation mode collapses. A proof-of-concept on Qwen2.5-Omni-3B preserves generation equivalence on a non-Qwen3.5 backbone and transfers image retrieval within 2-8 pp of Hydra-4B, with zero-shot audio retrieval emerging through the frozen Whisper encoder.