We use a joint optical/X-ray analysis to constrain the geometry and history of the ongoing merging event in the massive galaxy cluster MACSJ0416.1-2403 (z = 0.397). Our investigation of cluster substructure rests primarily on a combined strong-and weak-lensing mass reconstruction based on the deep, high-resolution images obtained for the Hubble Frontier Fields initiative. To reveal the system's dynamics, we complement this lensing analysis with a study of the intracluster gas using shallow Chandra data, and a three-dimensional model of the distribution and motions of cluster galaxies derived from over 100 spectroscopic redshifts. The multiscale grid model obtained from our combined lensing analysis extends the high-precision strong-lensing mass reconstruction recently performed to cluster-centric distances of almost 1 Mpc. Our analysis detects the two well-known mass concentrations in the cluster core. A pronounced offset between collisional and collisionless matter is only observed for the SW cluster component, while excellent alignment is found for the NE cluster. Both the lensing analysis and the distribution of cluster light strongly suggest the presence of a third massive structure, almost 2 arcmin SW of the cluster centre. Since no X-ray emission is detected in this region, we conclude that this structure is non-virialized and speculate that it might be part of a large-scale filament almost aligned with our line of sight. Combining all evidence from the distribution of dark and luminous matter, we propose two alternative scenarios for the trajectories of the components of MACSJ0416.1-2403. Upcoming deep X-ray observations that allow the detection of shock fronts, cold cores, and sloshing gas (all key diagnostics for studies of cluster collisions) will allow us to test, and distinguish between these two scenarios.