The first closure study involving passive microwave and submillimetre measurements of ice clouds with the consideration of oriented particles is presented, using a unique combination of polarised observations from the ISMAR spectral-like radiometer, two radars with frequencies of 35 and 95 GHz, and a variety of in situ instruments. Of particular interest to this study are the large V–H polarised brightness temperature differences measured from ISMAR above a thick frontal ice cloud. Previous studies combining radar and passive submillimetre measurements have not considered polarisation differences. Moreover, they have assumed particle habits a priori. We aim to test whether the large V–H measurements can be simulated successfully by using an atmospheric model consistent with in situ microphysics. An atmospheric model is constructed using information from the in situ measurements, such as the ice water content, the particle size distribution, and the mass and shape of particles, as well as background information obtained from dropsonde profiles. Columnar and dendritic aggregate particle models are generated specifically for this case, and their scattering properties are calculated using the independent monomer approximation under the assumption of horizontal orientation. The scattering properties are used to perform polarised radiative transfer simulations using ARTS to test whether we can successfully simulate the measured large V–H differences. Radar measurements are used to extrapolate the 1-D microphysical profile to derive a time series of particle size distributions which are used to simulate ISMAR brightness temperatures. These simulations are compared to the observations. It is found that particle models that are consistent with in situ microphysics observations are capable of reproducing the brightness temperature depression and polarisation signature measured from ISMAR at the dual-polarised channel of 243 GHz. However, it was required that a proportion of the particles were changed in order to increase the V–H polarised brightness temperature differences. Thus, we incorporated millimetre-sized dendritic crystals, as these particles were observed in the probe imagery. At the second dual-polarised channel of 664 GHz, the brightness temperature depressions were generally simulated at the correct locations; however, the simulated V–H was too large. This work shows that multi-frequency polarisation information could be used to infer realistic particle shapes, orientations, and representations of the split between single crystals and aggregates within the cloud.