The magnetic induction (MI)-based wireless underground sensor networks (WUSNs) use the novel MI waveguide technique to establish long range and low cost wireless communications in harsh underground environments, which enable a large variety of novel and important applications. One of the main research challenges is the theoretical study of the channel and network capacities in these networks. Compared to the traditional wireless networks, both the channel and network capacities of MI-based WUSNs have significant different characteristics due to the completely different signal propagation techniques and network geometric structure. Moreover, the usage of multiple resonant MI relay coils in MI-based WUSNs brings more reliability concerns. In this paper, mathematical models are developed to evaluate the channel capacity, network capacity, and the reliability of MI-based WUSNs. Specifically, the closed-form expression for the channel capacity in MI-based WUSNs is first derived to capture the effects of multiple system parameters. Then the network capacity scaling laws of MI-based WUSNs are investigated under different deployment strategies. Finally, the system reliability of MI-based WUSNs in terms of the channel capacity and network capacity is discussed. The results of this paper provide principles and guidelines for the design and deployment of MI-based WUSNs.