Pure rotational spectra of the ground vibrational states of ten isotopologues of each of H(2)O⋅⋅⋅CuCl and H(2)O⋅⋅⋅AgCl have been measured and analyzed to determine rotational constants and hyperfine coupling constants for each molecule. The molecular structure and spectroscopic parameters determined from the experimental data are presented alongside the results of calculations at the CCSD(T) level. Both experiment and theory are consistent with structures that are nonplanar at equilibrium. The heavy atoms are collinear while the local C(2) axis of the water molecule intersects the axis defined by the heavy atoms at an angle, φ = 40.9(13)° for Cu and φ = 37.4(16)° for Ag. In the zero-point state, each molecule is effectively planar, undergoing rapid inversion between two equivalent structures where φ has equal magnitude but opposite sign. The equilibrium geometry has C(s) symmetry, however. The ab initio calculations confirm that the timescale of this inversion is at least an order of magnitude faster than that of rotation of the molecule in the lowest rotational energy levels. The molecular geometries are rationalized using simple rules that invoke the electrostatic interactions within the complexes. Centrifugal distortion constants, Δ(J) and Δ(JK), nuclear quadrupole coupling constants, χ(aa)(Cu), χ(aa)(Cl), (χ(bb) - χ(cc))(Cu), and (χ(bb) - χ(cc))(Cl), and the nuclear spin-rotation constant of the copper atom, C(bb)(Cu)+C(cc)(Cu), are also presented.