  As recent observations of the molecular discs in spiral galaxies point to the
existence of a diffuse, low-density thick molecular disc along with the
prominent thin one, we investigate the observational signatures of this thick
disc by theoretically modelling two-component molecular discs in a sample of
eight nearby spiral galaxies. Assuming a prevailing hydrostatic equilibrium, we
set up and solved the joint Poisson's-Boltzmann equation to estimate the
three-dimensional distribution of the molecular gas and the molecular scale
height in our sample galaxies. The molecular scale height in a two-component
molecular disc is found to vary between $50-300$ pc, which is higher than what
is found in a single-component disc. We find that this scale height can vary
significantly depending on the assumed thick disc molecular gas fraction. We
also find that the molecular gas flares as a function of the radius and follows
a tight exponential law with a scale length of $\left(0.48 \pm 0.01 \right)
r_{25}$. We used the density solutions to produce the column density maps and
spectral cubes to examine the ideal observing conditions to identify a thick
molecular disc in galaxies. We find that unless the molecular disc is an
edge-on system and imaged with a high spatial resolution ($\lesssim 100$ pc),
it is extremely hard to identify a thick molecular disc in a column density
map. The spectral analysis further reveals that at moderate to high inclination
($i \gtrsim 40^o$), spectral broadening can fictitiously introduce the
signatures of a two-component disc into the spectral cube of a single-component
disc. Hence, we conclude that a low inclination molecular disc imaged with high
spatial resolution would serve as the ideal site for identifying the thick
molecular disc in galaxies.
