As combat scales up and weapons become more intelligent, airborne networks (AN) must facilitate high-precision communications. This means that the airborne network should have communication capability with minimum delay, low jitter, and high reliability, and this new type of AN is called an airborne time-sensitive network (ATSN). A prerequisite to guarantee the above communication capability is to have a high precision time synchronization protocol. To plug this gap, we have designed a software-defined airborne time-sensitive network (SD-ATSN) architecture based on the benefits of software-defined centralization and flexibility. It supports our proposed all-domain fusion-based time synchronization protocol (AF-TSP) to support precise time synchronization between ATSN platforms. In AF-TSP, we innovatively propose an all-domain (land, sea, air, and space) master clock hot standby mechanism to cope with the existing instability and poor robustness in AN. In the key problem of the master clock election, we first completed a rough election utilizing improved K-Means++. Subsequently, on top of the rough election, we inserted a mixed mutation operator to improve the convergence of the multiobjective optimization algorithm No Dominant Sorting Genetic Algorithm-II (NSGA-II). The control delay, clock accuracy, and path reliability coefficient are the optimization objectives for selecting the appropriate master clock. Simulation results demonstrate that our protocol has advantages in terms of synchronization precision, communication delay, and network robustness.