A joint earthquake source inversion technique is presented that uses InSAR and long-period teleseismic data, and, for the first time, takes 3-D Earth structure into account when modelling seismic surface and body waves. Ten average source parameters (Moment, latitude, longitude, depth, strike, dip, rake, length, width and slip) are estimated; hence, the technique is potentially useful for rapid source inversions of moderate magnitude earthquakes using multiple data sets. Unwrapped interferograms and long-period seismic data are jointly inverted for the location, fault geometry and seismic moment, using a hybrid downhill Powell-Monte Carlo algorithm. While the InSAR data are modelled assuming a rectangular dislocation in a homogeneous halfspace, seismic data are modelled using the spectral element method for a 3-D earth model. The effect of noise and lateral heterogeneity on the inversions is investigated by carrying out realistic synthetic tests for various earthquakes with different faulting mechanisms and magnitude (Mw6.0-6.6). Synthetic tests highlight the improvement in the constraint of fault geometry (strike, dip and rake) and moment when InSAR and seismic data are combined. Tests comparing the effect of using a 1-D or 3-D earth model show that long-period surface waves are more sensitive than long-period body waves to the change in earth model. Incorrect source parameters, particularly incorrect fault dip angles, can compensate for systematic errors in the assumed Earth structure, leading to an acceptable data fit despite large discrepancies in source parameters. Three real earthquakes are also investigated: Eureka Valley, California (1993 May 17, Mw6.0), Aiquile, Bolivia (1998 February 22, Mw6.6) and Zarand, Iran (2005 May 22, Mw6.5). These events are located in different tectonic environments and show large discrepancies between InSAR and seismically determined source models. Despite the 40-50 km discrepancies in location between previous geodetic and seismic estimates for the Eureka Valley and Aiquile earthquakes, the seismic data are found to be compatible with the InSAR location. A 30°difference in strike between InSAR and seismic-derived source models is also resolved when taking 3-D Earth structure into account in the analysis of the Eureka Valley earthquake. The combination of both InSAR and seismic data further constrains the dip for the Zarand earthquake, and in all cases the seismic moment is more robustly constrained in the joint inversions than in the individual data set inversions. Unmodelled lateral heterogeneities in Earth and the models could partly explain some of the observed source parameter discrepancies related to the seismic data. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.