The gas cycling in the circumgalactic regions of galaxies is known to be multi- phase. The MUSE-ALMA Haloes survey gathers a large multi-wavelength observational sample of absorption and emission data with the goal to significantly advance our understanding of the physical properties of such CGM gas. A key component of the MUSE-ALMA Haloes survey is the multi-facility observational campaign conducted with VLT/MUSE, ALMA, and HST. MUSE-ALMA Haloes targets comprise 19 VLT/MUSE IFS quasar fields, including 32 z_abs_<0.85 strong absorbers with measured N(H I) => 10^18^ cm^-2^ from UV-spectroscopy. We additionally use a new complementary HST medium program to characterize the stellar content of the galaxies through a 40-orbit three-band UVIS and IR WFC3 imaging. Beyond the absorber-selected targets, we detect 3658 sources all fields combined, including 703 objects with spectroscopic redshifts. This galaxy-selected sample constitutes the main focus of the current paper. We have secured millimeter ALMA observations of some of the fields to probe the molecular gas properties of these objects. Here, we present the overall survey science goals, target selection, observational strategy, data processing and source identification of the full sample. Furthermore, we provide catalogues of magnitude measurements for all objects detected in VLT/MUSE, ALMA, and HST broad-band images and associated spectroscopic redshifts derived from VLT/MUSE observations. Together, this data set provides robust characterization of the neutral atomic gas, molecular gas and stars in the same objects resulting in the baryon census of condensed matter in complex galaxy structures.