The long propagation delay presents a nonnegligible impact on medium access control (MAC) in underwater acoustic networks (UANs), leading to the coupling of spatial propagation delay and transmission time in determining frame collisions at receivers. To this end, this article first reveals the space-time coupling relationship for collision-free transmissions. We find that the interference region for simultaneous transmissions is an annulus, which is much smaller than the whole transmission range. Thus, UANs have more spatial multiplexing opportunities than terrestrial radio networks. By deriving the collision probabilities of the ALOHA-based protocols, we show that the annulus interference region in UANs provides potential to improve random access protocols. We further derive the heuristics for optimal scheduling for periodical transmissions under space-time coupling, which is formulated as a mixed-integer linear programming problem. The obtained heuristics are then used to design low-complexity algorithms, which are verified by simulation results. Our proposed algorithms can achieve the optimal scheduling in star networks and outperform the existing MAC in mesh networks.