  We construct a covariant formulation of the heterotic superstring on K3 times
T^2 with manifest N=2 supersymmetry. We show how projective superspace appears
naturally in the hybrid formulation giving a (partially) geometric
interpretation of the harmonic parameter. The low-energy effective action for
this theory is given by a non-standard form of N=2 supergravity which is
intimately related to the N=1 old-minimal formulation. This formalism can be
used to derive new descriptions of interacting projective superspace field
theories using Berkovits' open string field theory and the the heterotic
Berkovits-Okawa-Zwiebach construction.
