Horizontally propagating chemical fronts are studied in a thin solution layer of the acid-catalyzed chlorite-tetrathionate reaction. Unusual cellular patterns develop when significant amount of autocatalyst is bound to polyelectrolyte with low mobility: both oscillatory and stationary patterns evolve as a result of the interaction between the reaction front and the superposed gravity current. The concentration of the polyelectrolyte regulating the velocity of front propagation serves as a bifurcation parameter for switching between the two basic patterns.