With the increasing proliferation of different communication devices sharing the same spectrum, it is critical to understand the impact of interference in heterogeneous wireless networks. In this paper, we put forth a mathematical model for coexistence in networks composed of both narrowband (NB) and ultrawideband (UWB) wireless nodes, based on fundamental tools from stochastic geometry. Our model considers that the interferers are spatially scattered according to a Poisson field, and are operating asynchronously in a wireless environment. We first determine the statistical distribution of the aggregate interference for both cases of NB and UWB emitters. We then provide error probability expressions for two dual configurations: 1) a NB victim link subject to the aggregate UWB interference, and 2) a UWB victim link subject to the aggregate NB interference. The results show that while the impact of a single interferer on a link is often negligible due to restrictions on the transmitted power, the aggregate effect of multiple interferers may cause significant degradation. Therefore, aggregate interference must be considered to ensure coexistence in heterogeneous networks. The proposed analytical framework shows good agreement with physical-level simulations of the system.