We evaluated a joint contrast source inversion scheme for marine controlled-source electromagnetic (mCSEM) and magnetotelluric (MT) data based on a scattered field formulation. The scheme considered only contrasts in electric conductivity, and it allowed the medium to be transversely isotropic with a vertical symmetry axis. The method was based on the integral equation formulation of electromagnetic field propagation, and we demonstrated how the method solved the inverse problem of determining the conductivity structure of the subsurface. The method did not consider MT impedances as data input to inversion, but instead explicitly the field components, and the consequences of this approach, were discussed. Although there are challenges associated with source estimation and data noise, we found it easier to make connections to CSEM and it simplified some computational issues. Three synthetic examples were considered to demonstrate the method: a reservoir below an anisotropic overburden, a salt diapir, and a reservoir near a salt diapir. MT and CSEM data were first treated sequentially, first inverting the MT data and using the result as the initial model and in the regularization in CSEM inversion. The result of this approach was then compared to a joint inversion. The same approach was finally applied to a real data set. We found that sequential inversions in some situations produced similar results as joint inversions, and hence, joint inversion may not be necessary in all situations. Nonetheless, joint inversion could be useful for imaging salt diapirs and eventually hydrocarbons near salt. In particular, it was useful to map the spatial extent of the salt diapirs. It was, moreover, a useful tool for checking data consistency in different models with respect to several data types.