Dynamics of complex interfaces is investigated in a model of an oscill
atory medium. The moving interfacial zone separating two phases of hom
ogeneous oscillation consists of a phase with chaotic spatial and temp
oral behavior. As system parameters vary, the thickness of the interfa
ce grows until a phase transition occurs where the chaotic phase fills
the entire domain. The system behavior and its critical properties ar
e analyzed in terms of two coupled stochastic equations describing the
profiles that delimit the interfacial zone.