To date, existing studies that use multilayer networks, in their multiplex form, to analyse the structure of financial systems, have (i) considered the structure as a non-interconnected multiplex network, (ii) no mechanism of multichannel contagion has been modelled and empirically evaluated and (iii) no multichannel stabilisation strategies for pre-emptive contagion containment have been designed. This paper formulates an interconnected multiplex structure, and a contagion mechanism among financial institutions due to bilateral exposures arising from institutions' activity within different interconnected markets that compose the overall financial market. We design minimum-cost stabilisation strategies that act simultaneously on different markets and their interconnections, in order to effectively contain potential contagion progressing through the overall structure. The empirical simulations confirm their capability for containing contagion. The potential for multichannel contagion through the multiplex contributes more to systemic fragility than single-channel contagion, however, multichannel stabilisation also contributes more to systemic resilience than single-channel stabilisation.