Conversational agents have traditionally been developed for either task-oriented dialogue (TOD) or open-ended chitchat, with limited progress in unifying the two. Yet, real-world conversations naturally involve fluid transitions between these modes. To address this gap, we introduce TACT (TOD-And-Chitchat Transition), a dataset designed for transition-aware dialogue modeling that incorporates structurally diverse and integrated mode flows. TACT supports both user- and agent-driven mode switches, enabling robust modeling of complex conversational dynamics. To evaluate an agent's ability to initiate and recover from mode transitions, we propose two new metrics -- Switch and Recovery. Models trained on TACT outperform baselines in both intent detection and mode transition handling. Moreover, applying Direct Preference Optimization (DPO) to TACT-trained models yields additional gains, achieving 75.74\% joint mode-intent accuracy and a 70.1\% win rate against GPT-4o in human evaluation. These results demonstrate that pairing structurally diverse data with DPO enhances response quality and transition control, paving the way for more proactive and transition-aware conversational agents.