In this work we give an extension of Kauffman's NK-Landscapes to multiobjective MNK-Landscapes in order to study the effects of epistasis on the performance of multiobjective evolutionary algorithms (MOEAs). This paper focuses on the development of multiobjective random one-bit climbers (moRBCs). We incrementally build several moRBCs and analyze basic working principles of state of the art MOEAs on landscapes of increased epistatic complexity and number of objectives. We specially study the effects of Pareto dominance, non-dominance, and the use of memory and a population to influence the search. We choose an elitist non-dominated sorting multiobjective genetic algorithm (NSGA-II) as a representative of the latest generation of MOEAs and include its results for comparison. We detail the behavior of the climbers and show that population based moRBCs outperform NSGA-II for all values of M and K.