Ultra-narrowband (UNB) communications is an emerging paradigm that tackles two challenges to realizing massive Internet-of-things (IoT) connectivity over the unlicensed spectrum: the intra-network sharing, i.e., how the spectrum is shared among IoT devices, and the inter-network sharing, i.e., the coexistence of the IoT network with other incumbent networks. Specifically, intra-network sharing is enabled by using extremely narrowband signals to connect a massive number of IoT devices without any prior network synchronization. Further, to enhance robustness to incumbent interference, each IoT packet is sent multiple times, each at a different frequency within a single band. Nevertheless, the interplay between intra-network sharing and inter-technology coexistence at a large scale remains unclear. Thus, in this paper, we develop an analytical framework to model and analyze UNB networks. We use stochastic geometry to derive the probability of successful transmission, identifying the impact of intra- and inter-network interference on the performance. In addition to analyzing the existing single-band access protocols, we present two multiband schemes, where each BS listens to a single band for practical implementation. Different access protocols are further compared in terms of the transmission capacity, i.e., the maximum number of IoT devices a UNB protocol can support in the presence of incumbent networks. Several design insights are gleaned from the derived closed-form expressions, and simulation results are further provided to validate them.