An aerosol-generating system including a liquid storage portion is provided, the portion including a rigid housing holding a liquid aerosol-forming substrate, the housing having an opening and a fluid permeable heater assembly including a plurality of electrically conductive filaments, wherein the fluid permeable heater assembly is fixed to the housing and extends across the opening of the housing. The provided heater assembly that extends across an opening of a liquid storage portion allows for a robust construction that is relatively simple to manufacture and allows for a large contact area between the heater assembly and liquid aerosol-forming substrate. The heater assembly may be substantially flat, allowing for simple manufacture.
