Three Cu2+-containing coordination polymers were synthesized and characterized by experimental (X-ray diffraction, magnetic susceptibility, pulsed-field magnetization, heat capacity, and muon-spin relaxation) and electronic structure studies (quantum Monte Carlo simulations and density functional theory calculations). [Cu(HF2)(pyz)(2)]SbF6 (pyz = pyrazine) (1a), [Cu2F(HF)(HF2)(pyz)(4)](SbF6)(2) (1b), and [CuAg(H3F4)(pyz)(5)](SbF6)(2) (2) crystallize in either tetragonal or orthorhombic space groups; their structures consist of 2D square layers of [M(pyz)2](n+) that are linked in the third dimension by either HF2-(1a and 1b) or H3F4- (2). The resulting 3D frameworks contain charge-balancing SbF6- anions in every void. Compound 1b is a defective polymorph of la, with the difference being that 50% of the HF2- links are broken in the former, which leads to a cooperative Jahn-Teller distortion and d(x2-y2) orbital ordering. Magnetic data for 1a and 1b reveal broad maxima in chi at 12.5 and 2.6 K and long-range magnetic order below 4.3 and 1.7 K, respectively, while 2 displays negligible spin interactions owing to long and disrupted superexchange pathways. The isothermal magnetization, M(B), for I a and 1b measured at 0.5 K reveals contrasting behaviors: 1a exhibits a concave shape as B increases to a saturation field, B-c of 37.6 T, whereas 1b presents an unusual two-step saturation in which M(B) is convex until it reaches a step near 10.8 T and then becomes concave until saturation is reached at 15.8 T. The step occurs at two-thirds of M-sat, suggesting the presence of a ferrimagnetic structure. Compound 2 shows unusual hysteresis in M(B) at low temperature, although chi vs T does not reveal the presence of a magnetic phase transition. Quantum Monte Carlo simulations based on an anisotropic cubic lattice were applied to the magnetic data of la to afford g = 2.14, J = -13.4 K (Cu-pyz-Cu), and J(perpendicular to) = -0.20 K (Cu-F center dot center dot center dot H center dot center dot center dot F-Cu), while chi vs T for 1b could be well reproduced by a spin-1/2 Heisenberg uniform chain model for g = 2.127(1), J(1) = -3.81(1), and zJ(2) = -0.48(1) K, where J(1) and J(2) are the intra- and interchain exchange couplings, respectively, which considers the number of magnetic nearest-neighbors (z). The M(B) data for 1b could not be satisfactorily explained by the chain model, suggesting a more complex magnetic structure in the ordered state and the need for additional terms in the spin Hamiltonian. The observed variation in magnetic behaviors is driven by differences in the H center dot center dot center dot F hydrogen-bonding motifs.