Recently, new results on percolation in interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the percolation process might present a bistability of the equilibrium solution. To this end, we introduce antagonistic interactions for which the functionality, or activity, of a node in a network is incompatible with the functionality of the linked nodes in the other interacting networks. In particular, we study the percolation transition in two interacting networks with purely antagonistic interaction and differing topology.