  We present a model for the interpretation of the gamma-ray background
emission from the Galactic halo, which we attribute to interaction of
high-energy cosmic rays with dense molecular clumps. In a wide range of clump
parameters we calculate the expected gamma-photon flux, taking into account for
the first time optical depth effects. This allows us to derive new constraints
on masses and sizes of possible molecular clumps and their contribution to the
galactic surface density.
  The observed gamma-ray distribution can be explained best by models with a
flattened halo distribution of axis ratio ~ 0.3. If optical depth effects are
important, the clumps must have radii of ~ 6 AU and masses of ~ 10^{-3} M_sun.
This would result in a total mass of ~ 2 10^{11} M_sun for such clumps and
contribute with Sigma ~ 140 M_sun pc^{-2} to the local surface density.
