A multiphase cloud chemistry model coupling a detailed chemical reactivity mechanism in gas phase and aqueous phase to a cloud parcel model with a two-moment microphysical scheme has been extended to include ice phase processes. This newly developed model is used to study the influence of the ice phase on HCOOH, HNO3, H2O2 and CH2O in a mixed-phase cloud. Microphysical processes are describing the interactions between the water vapor phase, the liquid phase (cloud and rain water) and the ice phase (pristine ice, snow and graupel) in the cloud and for soluble chemical species, their transfer by mixed-phase microphysical processes has been included. In addition to microphysical transfer between iced hydrometeors, the probable two main processes incorporating soluble chemical species in iced hydrometeors are the retention in ice phase as riming or freezing occurs and the burial in the ice crystal as the crystal grows by vapor diffusion. The model is applied to a cloud event describing a moderate precipitating mixed-phase cloud forming in a continental air mass in winter. The main features of the cloud are described and the evolution of key chemical species as function of time and temperature is discussed. Sensitivity tests are performed: a run without ice to highlight the influence of ice phase on the chemical gas phase composition of the cloud, a run without burial showing that it is a negligible process, a run assuming full retention in ice for all species and a run varying the ice crystal shapes. A detailed analysis of the microphysical rates and chemical rates linked to retention and burial effects show that for this cloud event, the effect of the ice phase on gas phase composition is driven by riming of cloud droplets onto graupels, which leads to retention or not of soluble chemical species in the ice phase. Finally, the impact of crystal geometry on the efficiency of collection is studied together with its impact on the riming of cloud droplets on graupels and also on the retention of chemical species in ice phase.