With the increasing complexity and frequency of interactions among a large number of heterogeneous nodes within a combat system of systems (SoS), evaluating the capability of the SoS to withstand external attacks and interferences has become an increasingly challenging and urgent issue. However, the complexity of a combat SoS often brings about difficulties in quantitative analysis. This paper proposes a method to assess the resilience of a combat SoS. Firstly, a network model of a combat SoS is constructed, taking into account multi-functional composite nodes. Secondly, the combat capability model of the combat SoS is built based on the capabilities of the kill chains and kill networks. Lastly, an approach is proposed to calculate the combat capability of the system based on the network’s two-terminal connectivity. Moreover, based on the SoS’s combat capability, the resilience is analyzed from the dimensions of anti-destruction, survival, and recovery. The simulation experiments show that, compared to other methods, the method in this paper for calculating the combat capability of the combat SoS does not depend on the number of kill chains and aligns with the combat processes and actual patterns. Additionally, the resilience measurement method can effectively analyze its capability to cope with external interferences.