The formation of agents' opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand, the concurrent participation of agents to discussions on different topics induces each agent to develop a coherent set of opinions across all the topics in which he is active. Moreover, the pervasive action of external stimuli, such as mass media, pulls the entire population towards a specific configuration of opinions on different topics. Here we propose a model in which agents with interrelated opinions, interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhood, strive to maintain internal coherence, due to the fact that each agent identifies meaningful relationships among its opinions on the different topics, and are at the same time subject to external fields, resembling the pressure of mass media. We show that the presence of heterogeneity in the internal coupling assigned by agents to their different opinions allows to obtain states with mixed levels of consensus, still ensuring that all the agents attain a coherent set of opinions. Furthermore, we show that all the observed features of the model are preserved in the presence of thermal noise up to a critical temperature, after which global consensus is no longer attainable. This suggests the relevance of our results for real social systems, where noise is inevitably present in the form of information uncertainty and misunderstandings. The model also demonstrates how mass media can be effectively used to favour the propagation of a chosen set of opinions, thus polarising the consensus of an entire population.