Waveform inversion aims to retrieve high-resolution earth parameter volumes. Due to its high computational cost, acoustic approaches using low to mid seismic data frequencies are often applied in velocity model building. However, in the presence of large parameter contrasts, an elastic formulation should be preferred due to wave interferences that limit the applicability of phase- and kinematics-only approaches. The benefits of elastic waveform inversion have been demonstrated with inversion of hydrophone data in marine environments. Here, we extend the approach to inversion of the vertical geophone component. We propose a weighted cost function in the waveform inversion algorithm to jointly invert multicomponent data sets, and we compare the results to the inversion of single-component data. For this study, we use an ocean-bottom-node data set from the deepwater Gulf of Mexico around a salt dome. We show that slightly different velocity models, reverse time migration images, and angle gathers are retrieved when using hydrophone or vertical geophone data, further improving either the shallow or deeper sediments. The joint inversion combines the improvements brought by the single-component inversions. Though it doubles the cost, joint elastic waveform inversion of hydrophone and vertical geophone data can help velocity model building around salt bodies.