  We prove positive mass theorem with angular momentum and charges for axially
symmetric, simply connected, maximal, complete initial data sets with two ends,
one designated asymptotically flat and the other either (Kaluza-Klein)
asymptotically flat or asymptotically cylindrical, for 4-dimensional
Einstein-Maxwell theory and $5$-dimensional minimal supergravity theory which
metrics fail to be $C^1$ and second fundamental forms and electromagnetic
fields fail to be $C^0$ across an axially symmetric hypersurface $\Sigma$.
Furthermore, we remove the completeness and simple connectivity assumptions in
this result and prove it for manifold with boundary such that the mean
curvature of the boundary is non-positive.
