Disclosed is a coextruded, fire-resistant, composite structure of adjacent, alternating first and second layers wherein the first layer comprises a thermoplastic foam and second layer a thermoplastic material with such second layers containing a quantity of a brominated fire retardant sufficient to enhance the flame retardancy of the composite structure. Incorporation of the fire retardant into the thermoplastic material layers allows a fire-resistant foam structure to be made using water as a blowing agent for the first layers while avoiding serious corrosion problems encountered when incorporating both brominated fire retardants and water in the same foam structure. Further disclosed are processes for making the above described composite structure. Further disclosed is a composite flow melt expandable into the above-described composite structure.