Complexes of H3NCuF and H3NCuI have been synthesised in the gas phase and characterized by microwave spectroscopy. The rotational spectra of 4 isotopologues of H3NCuF and 5 isotopologues of H3NCuI have been measured in the 6.5-18.5 GHz frequency range using a chirped-pulse Fourier transform microwave spectrometer. Each complex is generated from a gas sample containing NH3 and a halogen-containing precursor diluted in Ar. Copper is introduced by laser ablation of a solid target prior to supersonic expansion of the sample into the vacuum chamber of the microwave spectrometer. The spectrum of each complex is characteristic of a symmetric rotor and a C3v geometry in which the N, Cu and X atoms (where X is F or I) lie on the C axis. The rotational constant (B0), centrifugal distortion constants (DJ and DJK), nuclear spin-rotation (Cbb(Cu) = Ccc(Cu)) constant (for H3NCuF only) and nuclear quadrupole coupling constants (χaa(X) where (X = N, Cu, I)) are fitted to the observed transition frequencies. Structural parameters are determined from the measured rotational constants and also calculated ab initio at the CCSD(T)(F12*)/AVQZ level of theory. Force constants describing the interaction between ammonia and each metal halide are determined from DJ for each complex. Trends in the interaction strengths and geometries of BCuX (B = NH3, CO) (X = F, Cl, Br, I) are discussed.