This paper presents a novel framework that mathematically and optimally quantifies demand response (DR) provisions, considering the power availability of Internet of Things (IoT)-based house load management for the provision of flexibility in the smart grid. The proposed framework first models house loads using IoT windows and occupant behavior, and then integrates IoT-based house loads into DR programs based on a novel mathematical optimization model to provide the optimal power flexibility considering the penetration of IoT-based houses in distribution systems. Numerical results that consider a 33-bus distribution system are reported and discussed to demonstrate the effectiveness of flexibility provisions, from integrating IoT-based houses into DR programs, on peak load reduction and system capacity enhancement.