We calculate the exact analytical solution to the domain wall properties in a multiferroic system with two order parameters that are coupled bi-quadratically. This is then adapted to the case of a magnetoelectric multiferroic material such as BiFeO3, with a view to examine critically whether the domain walls can account for the enhancement of magnetization reported for thin films fo this material, in view of the correlation between increasing magnetization and increasing volume fraction of domain walls as films become thinner. The present analysis can be generalized to describe a class of magnetoelectric devices based upon domain walls rather than bulk properties.