In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables.