Soft hydrogel particles show a rich structural and mechanical behaviour compared to hard particles, both in bulk and when confined in two dimensions at a fluid interface. Moreover, encapsulation into hydrogel shells makes it possible to transfer the tunability of soft steric interactions to hard nanoparticle cores, which bear interest for applications, e.g. in terms of optical, magnetic and reinforcement properties. In this work, we investigate the dependence of the microstructures formed by hard core-soft shell particles at liquid-liquid interfaces upon compression. We produced model particles with the same silica core and systematically varied the shell-to-core ratio by synthesising shells with three different thicknesses. These particles were spread at an oil-water interface in a Langmuir-Blodgett trough and continuously transferred onto a solid support during compression. The transferred microstructures were analysed by atomic force and scanning electron microscopy. Quantitative image analysis provided information on the particle packing density, the inter-particle distance, and the degree of order of the monolayers. We discovered several essential differences compared to purely soft hydrogel particles, which shed light on the role played by the hard cores in the assembly and compression of these composite monolayers.