The morphological approach is a computationally attractive method for calculating relative permeability and capillary pressure saturation functions. In the corresponding workflow, morphological operations are used to calculate the fluid phase distribution in the pore space of a digital twin. Once the pore space is occupied, the conductivity of the individual fluid phases and thus the relative permeability can be calculated by direct flow simulations. It therefore combines computationally favorable geometric operations with direct flow simulations. In contrast to pore network modeling, all calculations are directly performed on the digital twin without abstraction of the pore space. While the morphological operations conceptually correctly describe primary drainage processes and delivers good results, the method so far failed to describe imbibition processes and the influence of wettability. In this work, we implement contact angle distributions in a deterministic and stochastic way. In this manner, we extend the simulated saturation range from purely spontaneous to forced imbibition, resulting in a full-range imbibition relative permeability. Furthermore, by introducing stochastic contact angle distributions, different fluid phase distributions are obtained, which now allow for an uncertainty analysis. To verify the simulation results, we check (a) whether the simulation results agree with SCAL measurements and (b) compare morphologically and experimentally derived results on the pore scale. With the newly introduced concepts, the imbibition process behaves as physically expected, and shows a good agreement with experimentally derived relative permeability curves and microscopic fluid-phase distributions.