Estimation of seismic velocities and subsurface reservoir properties in deep, complex, geologic environments calls for the coordination of new acquisition technology with novel depth-domain inversion methods. Here, we propose a method for inversion of subsurface reflectivity image gathers that jointly relies on broadband data acquired by multimeasurement methods (vector-acoustic data; pressure and its gradients) from monopole (pressure) and dipole (e.g., gradient) sources. Our inversion retrieves depth-domain extended images (EIs), which represent the full nonlinear reflectivity operators with pseudosources and pseudoreceivers within the subsurface, as a function of time or frequency. Based on recent advances in interferometry by multidimensional deconvolution (MDD), we present two MDD-based imaging conditions for an EI inversion. One imaging condition consists of deconvolving correlation-based EIs with the so-called joint point-spread function (JPSF). These methods can, in principle, account for imaging primaries as well as internal and free-surface multiples. Because it is based on MDD, our JPSF approach can fully account for blended/simultaneous-source data in imaging with no need to deblend/separate the simultaneous-source data prior to imaging. Using dual-source vector-acoustic data, we describe how the EI JPSF system is constructed by separating source and receiver wavefields from receiver-side upgoing and ghost data, from pressure and gradient sources. With numerical examples, we demonstrate how the method successfully inverts for EIs representing subsurface reflectivity, while benefiting from the increase in temporal and spatial bandwidth brought on by the joint use of dual-source vector-acoustic data. Although here we focus on broadband streamer seismic applications, our joint wavefield inversion approach provides a framework for jointly imaging data from multiple experiments of any kind (e.g., surface and borehole, active and passive) with acoustic, elastic, and electromagnetic fields.