Network ecology is a rising field of quantitative biology representing ecosystems as complex networks. A suitable example is parasite spreading: several parasites may be transmitted among their hosts through different mechanisms, each one giving rise to a network of interactions. Modelling these networked, ecological interactions at the same time is still an open challenge. We present a novel spatially embedded multiplex network framework for modelling multi-host infection spreading through multiple routes of transmission. Our model is inspired by Trypanosoma cruzi , a parasite transmitted by trophic and vectorial mechanisms. Our ecological network model is represented by a multiplex in which nodes represent species populations interacting through a food web and a parasite contaminative layer at the same time. We modelled Susceptible-Infected dynamics in two different scenarios: a simple theoretical food web and an empirical one. Our simulations in both scenarios show that the infection is more widespread when both the trophic and the contaminative interactions are considered with equal rates. This indicates that trophic and contaminative transmission may have additive effects in real ecosystems. We also find that the ratio of vectors-to-host in the community (i) crucially influences the infection spread, (ii) regulates a percolating phase transition in the rate of parasite transmission and (iii) increases the infection rate in hosts. By immunizing the same fractions of predator and prey populations, we show that the multiplex topology is fundamental in outlining the role that each host species plays in parasite transmission in a given ecosystem. We also show that the multiplex models provide a richer phenomenology in terms of parasite spreading dynamics compared to more limited mono-layer models. Our work opens new challenges and provides new quantitative tools for modelling multi-channel spreading in networked systems.