  We extend recent numerical results (Dobbs et. al. 2006) on molecular cloud
formation in spiral galaxies by including a multi-phase medium. The addition of
a hot phase of gas enhances the structure in the cold gas, and significantly
increases the fraction of molecular hydrogen that is formed when the cold gas
passes through a spiral shock. The difference in structure is reflected in the
mass power spectrum of the molecular clouds, which is steeper for the
multi-phase calculations. The increase in molecular gas occurs as the addition
of a hot phase leads to higher densities in the cold gas. In particular, cold
gas is confined in clumps between the spiral arms and retains a higher
molecular fraction. Unlike the single phase results, molecular clouds are
present in the inter-arm regions for the multi-phase medium. However the
density of the inter-arm molecular hydrogen is generally below that which can
be reliably determined from CO measurements. We therefore predict that for a
multi-phase medium, there will be low density clouds containing cold atomic and
molecular hydrogen, which are potentially entering the spiral arms.
