The resultant field on the x-y plane will be the superposition of the field due to the two charged hemispheres. The direction of field on the points in x-y plane will be long negative z-axis.

As the field is along negative z-axis the plane of x-y plane will be a equipotential surface.

For the points on the z-axis outside the sphere the two hemispheres can be considered as point charges, the two points will act as a dipole.

So the field at the points at z-axis will be along the dipole moment that is along positive z-direction.