In combined electrical and heat networks (CEHNs) under the Islanded mode, the district heating network (DHN) is more vulnerable to fluctuations in the electrical load, resulting in the transgression of the CHEN power flow. Identifying vulnerable areas in islanded CEHNs is necessary. In this paper, we introduce a static sensitivity analysis method into islanded CHENs, which can identify vulnerable areas susceptible to these impacts, and explore the energy interaction mechanisms between the electrical network (EN) and DHN. We established a power flow model of the islanded CEHN, and developed the sensitivity matrix. Then, the decomposition model is solved, based on which the static sensitivity matrices can be calculated. The case study shows that the sensitivity can effectively represent the impact of EN load changes on the mass flow rate of the DHN, thus we can locate the weak areas of the CEHN. It can provide auxiliary information for the safe and stable operation of an islanded CEHN, with fewer calculations compared to the power flow calculation method. In addition, the results present the enhancement of islanded CHEN stability by using a kind of combination of CHP units.