Composite multiferroics are an exciting class of engineered materials with a wide range of existing and potential applications. This paper describes an original finite element (FE) simulation for composite multiferroic devices. Detailed analysis is given on the flow of electric/magnetic fields between the composite regions with attention given to the conductivity of the magnetostrictive layers (piezoelectric assumed to be insulating). The simulation is verified against an existing FE code and against a theoretical analysis, also presented here. The issue of boundary and continuity conditions is discussed in detail and approximations made in both FE and analytical treatments are specified. We derive the I-V curves of the composite device when acting as a magnetic field detector, in both conducting and insulating cases. The magnetic field detector acts as a voltage source: we calculate its open-circuit voltage and internal impedance in each case.