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Reliable transcription of child-adult conversations in clinical settings is crucial for diagnosing developmental disorders like Autism. Recent advances in deep learning and availability of large scale transcribed data has led to development of speech foundation models that have shown dramatic improvements in ASR performance. However, their performance on conversational child-adult interactions remains underexplored. In this work, we provide a comprehensive evaluation of ASR performance on a dataset containing child-adult interactions from autism diagnostic sessions, using Whisper, Wav2Vec2, HuBERT, and WavLM. We find that speech foundation models show a noticeable performance drop (15-20% absolute WER) for child speech compared to adult speech in the conversational setting. Then, we fine-tune the best-performing zero-shot model (Whisper-large) using LoRA in a low-resource setting, yielding 8% and 13% absolute WER improvements for child and adult speech, respectively.