Underwater acoustic communication networks (UACNs) are considered a key enabler to the underwater internet of things (UIoT). UACN is regarded as essential for various marine applications such as monitoring, exploration, and trading. However, a large part of existing literature disregards the 3-dimensional (3D) nature of the underwater communication system. In this paper, we propose a K-tier UACN that acts as a gateway that connects the UIoT with the Space-Air-GroundSea Integrated System (SAGSIS). The proposed network architecture consists of several tiers along the vertical direction with adjustable depths. On the horizontal dimension, the best coverage probability (CP) is computed and maximized by optimizing the densities of surface stations (SSs) in each tier. On the vertical dimension, the depth of each tier is also optimized to minimize inter-tier interference and maximize overall system performance. Using tools from stochastic geometry, the total CP of the proposed K-tier network is analyzed. For given spatial distribution of UIoT device’s depth, the best CP can be achieved by optimizing the depths of the transceivers connected to the SSs through a tether. We verify the accuracy of the analysis using Monte-Carlo simulations. In addition, we draw multiple useful system-level insights that help optimize the design of underwater 3D networks based on the given distribution of UIoT device’s depths.