Offshore seismic and electromagnetic (EM) imaging for hydrocarbons can require up to tens of millions of parameters to describe the 3D distribution of complex seabed geology and relevant geophysical attributes. The imaging and data volumes for such problems are enormous. Descent-based methods are the only viable imaging approach, where it is often challenging to manage the convergence of stand-alone seismic and EM inversion experiments. When a joint seismic-EM inversion is implemented, convergence problems with descent-based methods are further aggravated. Moreover, resolution mismatches between seismic and EM pose another challenge for joint inversion. To overcome these problems, we evaluated a coupled seismic-EM inversion workflow and applied it to a set of full-wave-seismic, magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data for subsalt imaging. In our workflow, we address disparate resolution properties between seismic and EM data by implementing the seismic inversion in the Laplace domain, where the wave equation is transformed into a diffusion equation. The resolution of seismic data thus becomes comparable to that of EM data. To mitigate the convergence problems, the full joint seismic-EM inverse problem is split into manageable components: separate seismic and EM inversions and an intermediate step that enforces structural coupling through a cross-gradient-only inversion and resistivity-velocity crossplots. In this workflow, stand-alone seismic and MT inversion are performed first. The cross-gradient-only inversion and the crossplots are used to precondition the resistivity and velocity models for subsequent stand-alone inversions. By repeating the sequence of the stand-alone seismic, MT, and cross-gradient-only inversions along with the crossplots, we introduce the seismic structural information into the resistivity model, and vice versa, significantly improving the salt geometry in both resistivity and velocity images. We conclude that the improved salt geometry can then be used to precondition a starting model for CSEM inversions, yielding significant improvement in the resistivity images of hydrocarbon reservoirs adjacent to the salt.