The extreme weather disaster is a main threat to the operation of integrated electricity and heat systems (IEHSs), particularly the cold wave, which is prone to cause surges in regional demand for heat and electricity. In IEHSs, Internet data centers (IDCs) consume a huge amount of electricity and generate waste heat. The former can be regulated spatially by migrating workloads in the interconnected data network and interrupted temporally with the equipped backup generators or uninterruptible power supply (UPS), the latter can be captured and supplied to the districts using heat pump facilities. Thus, the energy behaviors of IDCs are impressively responsive, which are completely considered and dispatched to enhance the resilience of IEHSs against cold waves in this paper. Firstly, the integrated energy response (IER) meaning responsive electricity consumption and heat production of IDCs is modelled considering workload scheduling and emergency standby power supply. Secondly, the adverse impacts of cold waves on IEHS operation are comprehensively formulated considering both component outages and sudden increases in electricity and heat demand. The uncertain intensity and influence scope of the cold waves are characterized using intervals. Moreover, a scenario-based stochastic optimization model with interval parameters is constructed incorporating IER formulations, in which both unit commitment plan of IEHSs and IER strategies of IDCs are simultaneously optimized. Furthermore, a two-stage stochastic-interval solution method is proposed to handle the hybrid heterogeneous uncertainties in the model based on the L-shaped algorithm and interval linear programming theory. Numerical studies demonstrate the effectiveness of the proposed techniques using a test IEHS composed of IEEE 118-bus system, seven 32-node heating systems, and eight IDCs.