Completing Emil's observation: Take any subgraph isomorphism problem (well known to be NP-complete).  Add a new vertex in the middle of each edge and then orient the new edges outwards from the new vertex.  That is, replace each undirected edge $x-y$ by $x\leftarrow z\rightarrow y$.  I think you get two posets (with two levels) for which the subposet problem is equivalent to the original.  So it is NP-complete.