Autoregressive generation of interleaved text and acoustic tokens is a common approach to spoken-response generation in speech large language models. Although this design enables streaming generation with explicit textual guidance, generated acoustic tokens become part of the context for subsequent text predictions. Given identical speech inputs, we observe markedly lower answer accuracy for the internal text generated in speech-to-text-and-speech (S2TS) mode than for speech-to-text (S2T) responses. We term this discrepancy the \emph{output-mode gap} (OMG). To reduce OMG, we propose \emph{Joint-Output On-Policy Distillation} (JO-OPD), which distills the model's stronger S2T policy into joint generation using student-generated S2TS trajectories. At each text position, the S2T teacher provides soft targets from a text-only projection of the student's preceding outputs, while the student predicts from the corresponding full interleaved history. A preservation objective further regularizes native non-text predictions. Experiments on Step-Audio-2-mini and Baichuan-Audio-Instruct reveal OMG across two interleaved generation architectures. On Step-Audio-2-mini, JO-OPD reduces OMG from 42.87 to 16.26 percentage points on Spoken-MQA and from 29.72 to 13.04 points on speech-rendered GSM8K, with little change in S2T accuracy and substantially larger reductions than matched SFT baselines. ASR-based evaluation further shows a 7.49-point improvement in spoken-answer accuracy on Spoken-MQA.

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