The integrated electricity and heat system (IEHS) is an emerging demand-side flexible resource for power systems. IEHS operators participating in electricity markets considering their capabilities in reserve provision will face the reserve deliverability risk due to the energy-limited storage nature of heat systems. To address this challenge and increase profitability, a distributionally robust joint chance-constrained mechanism with enhanced quantifications is adopted for the heating system and reserve deployment uncertainties. Detailed pipeline storage representation for thermal networks and integrated demand response are incorporated into this strategic participation model. A two-stage distributionally robust joint chance constrained program is then incorporated to effectively manage the reserve deliverability risk by addressing uncertainties from local distributed energy resources and real-time reserve requests. The L-shaped algorithm is then customized by incorporating bi-linear Benders' decomposition and modified scenario filtering method to efficiently tackle solution challenges for the sophisticated model. Numerical results show the advantages of our approach in virtual thermal storage utilization, risk management, computational performance enhancement and scalability.