Bulk superconductivity has been achieved in the Hg-containing cuprates of (Pb0.5Hg0.5)(Sr2-xLax)CuO5-δ (1201~type) and (Pb0.5Hg0.5)Sr2(Ca1-xYx)Cu2O7-δ(1212-type) which exhibit Tc's around 30 K and 90 K for x = 1.2 in the 1201 system and x = 0.3 in the 1212 system, respectively. The detailed chemical compositions and crystal structures of such newly discovered IIg-containing superconducting phases have been studied by X-ray diffraction (XRD) including the Rietveld refinement analysis. The disorder of the hole reservoir layer (Pb,Hg)O was found by the analysis. The chemical substitutions of La^3+ into the Sr^2+ sites in the 1201 system and Ca^2+ into the Y^3+ sites in the 1212 system lead to optimise the hole concentration in the conducting CuO2 planes and enhance superconducting transition temperature.