Accurate transcription and speaker role diarization of child-adult spoken interactions are crucial for developmental and clinical research. However, manual annotation is time-consuming and challenging to scale. Existing automated systems typically rely on cascaded speaker diarization and automatic speech recognition pipelines, which can lead to error propagation. This paper presents a unified end-to-end framework that extends the Whisper encoder-decoder architecture to jointly model ASR and child-adult speaker role diarization. The proposed approach integrates: (i) a serialized output training scheme that emits speaker tags and start/end timestamps, (ii) a lightweight frame-level diarization head that enhances speaker-discriminative encoder representations, (iii) diarization-guided silence suppression for improved temporal precision, and (iv) a state-machine-based forced decoding procedure that guarantees structurally valid outputs. Comprehensive evaluations on two datasets demonstrate consistent and substantial improvements over two cascaded baselines, achieving lower multi-talker word error rates and demonstrating competitive diarization accuracy across both Whisper-small and Whisper-large models. These findings highlight the effectiveness and practical utility of the proposed joint modeling framework for generating reliable, speaker-attributed transcripts of child-adult interactions at scale. The code and model weights are publicly available

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