The ISA doesn't explicitly define humidity. There is a perfect gas assumption in the pressure lapse rate that implies dry air, but that's not relevant to calculations of performance etc based on ISA.
It nominally represents the average worldwide atmospheric profile in terms of pressure and temperature vs altitude to provide a normalising parameter for performance calculations etc.
If you actually had ISA conditions, then the air would be stable if it remained unsaturated as the actual lapse rate is lower than the convective lapse rate, as you describe.