With the increase in multi-energy loads and renewable energy (RE) penetration, the valley-to-peak value of the electric-heat system is gradually increasing. Although the integrated energy system (IES) and power-to-hydrogen (P2H) technology are widely used to improve energy efficiency and promote the consumption of REs, the dispatch strategies for the IES with P2H to provide integrated demand response (IDR) are not investigated clearly. Thus, this paper presents an optimal dispatch strategy for the IES to provide IDR with multiple P2H technologies. Firstly, a unified mathematical model is built for describing multiple P2H technologies with joint consideration of start/shutdown and ramping constraints. Then, a bi-level P2H-coupled IDR dispatch model is built where the upper level is the IES model including P2H and hydrogen storages with consideration of electric/gas/thermal multi-energy coupling, and the lower level is a flexible user model including transferrable and reduced loads. The Karush–Kuhn–Tucker (KKT) condition and big M methods are used to reformulate the lower-level user model into several complementary relaxation constraints. Then, the whole model is transferred into a solvable single level and linearized model. Finally, the case study shows that the proposed method can improve system flexibility and effectively reduce load peak-to-valley difference. Besides, the addition of P2H and HS into the IES can further optimize the whole economic profits, energy efficiency, and ability to consume REs.