  Constraints on the clustered mass density \Omega_m of the universe derived
from the mean intracluster gas fraction of X-ray clusters may be biased by a
single-phase assumption for the thermodynamic structure of the intracluster
medium (ICM). We propose a descriptive model for multiphase structure in which
a spherically symmetric ICM contains isobaric density perturbations with
radially dependent variance \sigma^2(r)=\sigma_c^2 (1+r^2/r_c^2)^{-\eps}. The
model extends the work of Gunn & Thomas (1996) which assumed radially
independent density fluctuations thoughout the ICM. Fixing the X-ray emission
profile and emission weighted temperature, we explore two independently
observable signatures of the model in the {\sigma_c,\eps} space. For
bremsstrahlung dominated emission, the central Sunyaev--Zeldovich (SZ)
decrement in the multiphase case is increased over the single-phase case and
multiphase X-ray spectra in the range 0.1-20 keV are flatter in the continuum
and exhibit stronger low energy emission lines than their single-phase
counterpart. We quantify these effects for a fiducial 10^8 K cluster and
demonstrate how the combination of SZ and X-ray spectroscopy can be used to
identify a preferred location in the {\sigma_c,\eps} plane. From these
parameters, the correct value of mean ICM gas fraction in the multiphase model
results, allowing an unbiased estimate of \Omega_m to be recovered. The
consistency of recent determinations of the Hubble constant from SZ and X-ray
observations with values determined by other methods suggests that biases in
ICM gas fractions are small, \ltsim 20%.
