Ambient radio frequency (RF) energy harvesting has emerged as a promising solution for powering small devices and sensors in massive Internet of Things (IoT) ecosystem due to its ubiquity and cost efficiency. In this paper, we study joint uplink and downlink coverage of cellular-based ambient RF energy harvesting IoT where the cellular network is assumed to be the only source of RF energy. We consider a time division-based approach for power and information transmission where each time-slot is partitioned into three sub-slots: 1) charging sub-slot during which the cellular base stations (BSs) act as RF chargers for the IoT devices, which then use the energy harvested in this sub-slot for information transmission and/or reception during the remaining two sub-slots; 2) downlink sub-slot during which the IoT device receives information from the associated BS; and 3) uplink sub-slot during which the IoT device transmits information to the associated BS. For this setup, we characterize the joint coverage probability, which is the joint probability of the events that the typical device harvests sufficient energy in the given time slot and is under both uplink and downlink signal-to-interference-plus-noise ratio (SINR) coverage with respect to its associated BS. This metric significantly generalizes the prior art on energy harvesting communications, which usually focused on downlink or uplink coverage separately. The key technical challenge is in handling the correlation between the amount of energy harvested in the charging sub-slot and the information signal quality (SINR) in the downlink and uplink sub-slots. Dominant BS-based approach is developed to derive tight approximation for this joint coverage probability. Several system design insights including comparison with regularly powered IoT network and throughput-optimal slot partitioning are also provided.