Device density in wireless internet of things (IoT) networks is now rapidly increasing and is expected to continue in the coming years. As a consequence, interference is a crucial limiting factor on network performance. This is true for all protocols operating on ISM bands (such as SigFox and LoRa) and licensed bands (such as NB-IoT). In this paper, with the aim of improving system design, we study the statistics of the interference due to devices in IoT networks; particularly those exploiting NB-IoT. Existing theoretical and experimental works have suggested that interference on each subband is well-modeled by impulsive noise, such as α-stable noise. If these devices operate on multiple partially overlapping resource blocks-which is an option standardized in NB-IoT-complex statistical dependence between interference on each subband is introduced. To characterize the multivariate statistics of interference on multiple subbands, we develop a new model based on copula theory and demonstrate that it effectively captures both the marginal α-stable model and the dependence structure induced by overlapping resource blocks. We also develop a low complexity estimation procedure tailored to our interference model, which means that the copula model can often be expressed in terms of standard network parameters without significant delays for calibration. We then apply our interference model in order to optimize receiver design, which provides a tractable means of outperforming existing methods for a wide range of network parameters.