Edit
Use the suggestion by @J.M.'spersistentexhaustion Prolog instead of Epilog.
ListPlot[{data1, data2}, Joined -> True, Mesh -> All,
EpilogProlog -> {Yellow, Polygon@Join[data1, Reverse@data2]}]
ListPlot[{data1, data2}, Joined -> True, Mesh -> All,
Epilog -> {Yellow, Polygon@Join[data1, Reverse@data2]}]
Edit
Use the suggestion by @J.M.'spersistentexhaustion Prolog instead of Epilog.
ListPlot[{data1, data2}, Joined -> True, Mesh -> All,
Prolog -> {Yellow, Polygon@Join[data1, Reverse@data2]}]