Constraints on the clustered mass density ��_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 ��^2(r)=��_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 {��_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 {��_c,\eps} plane. From these parameters, the correct value of mean ICM gas fraction in the multiphase model results, allowing an unbiased estimate of ��_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%.

Nine pages, submitted to Monthly Notices of the RAS. Seven postscript figures incoporated