Generalization of a Markov random field and a Bayesian network?


I am seeking a graphical model that is a generalization of both a Markov random field (MRF) and a Bayesian network (BN).

From the Markov random field wiki page:

A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can’t represent certain dependencies that a Bayesian network can (such as induced dependencies).

From the above description, particularly the last sentence, it appears that neither MRFs nor BNs are more general than the other.

Question: Is there a graphical model that encompasses both MRFs and BNs?

I believe such a graphical model will need to be directed so as to be able to model the (undirected) dependencies in a MRF (by included a directed edge in each direction).