  We investigate the quantum phase transitions in two capacitively coupled
two-dimensional Josephson-junction arrays with charge frustration. The system
is mapped onto the S=1 and $S=1/2$ anisotropic Heisenberg antiferromagnets near
the particle-hole symmetry line and near the maximal-frustration line,
respectively, which are in turn argued to be effectively described by a single
quantum phase model. Based on the resulting model, it is suggested that near
the maximal frustration line the system may undergo a quantum phase transition
from the charge-density wave to the super-solid phase, which displays both
diagonal and off- diagonal long-range order.
