Coupled models simulate different compartments of the Earth system as well as their interactions. For example coupled ocean-biogoechemical models simulate ocean circulation, biogeochemical processes and the carbon cycle. Coupled atmosphere-ocean models like the AWI Climate Model (AWI-CM), simulate the physics in both compartments and fluxes in between then. Data assimilation is used with coupled models to generate model fields to initialize model predictions, for computing a model state over time as a reanalysis, to optimize model parameters, and to assess model deficiencies. Ensemble data assimilation methods can be applied with these model systems, however the need to compute an ensemble of model integrations strongly increases the already high computing cost of the models. To allow us to perform the data assimilation in supercomputers, the parallel data assimilation framework (PDAF) has been developed. I will discuss the application and challenges of coupled ensemble data assimilation with PDAF on the example of two different coupled model systems: the ocean-biogeochemical model MITgcm-REcoM and the atmosphere-ocean model AWI-CM.