A deterministic cross-domain transmission architecture and a deep reinforcement learning(DRL)-based scheduling algorithm are proposed to address the cross-domain transmission problem in time-sensitive networks. The deterministic cross-domain transmission architecture is a wide-area deterministic networking architecture that integrates cyclic queuing forwarding with deterministic Internet Protocol. By defining a cross-domain cycle mapping function, a time-slot-based deterministic transmission channel is established to ensure bounded transmission delay. DRL states, actions, and rewards are detined in the DRL-based time-slot path joint online scheduling algorithm, and the scheduling target is to maximize the total earning value of all scheduled flows with different earning values. Experimental results demonstrate that the proposed cross-domain transmission architecture and scheduling algorithm can ensure end-to-end deterministic transmission, significantly improve the earning value of traffic scheduling, and guarantee the transmission of important traffic.