Full-duplex dialog models aim to listen and speak simultaneously, delivering rapid responses to dynamic user input. Among different solutions to full-duplexity, a native solution merges multiple channels in each time step, achieving the lowest latency. However, prevailing designs break down the textual monologue sentences for word-level alignment with audio streams, which degrades language modeling abilities. To help address this issue, we introduce "contiguous monologues", which are composed by continuous sentences and "waiting" intervals, mimicking human-like cognitive behavior in dialogs. We find a proper training paradigm to be critical for semantically aligning contiguous monologues with audio. To this end, we develop a "dual" training paradigm that alternates the position of the monologues, either leading or trailing the audio, across different training stages. A combination of our contiguous monologue and dual training strategy is applied in developing FLM-Audio, our 7B spoken dialog chatbot with native full-duplexity. As confirmed by experimental results, FLM-Audio achieves superior response qualities and chatting experiences while requiring significantly less training data.