The ALPINE-ALMA large program targets the [CII] 158um line and the far-infrared continuum in 118 spectroscopically confirmed star-forming galaxies between z=4.4 and z=5.9. It represents the first large [CII] statistical sample built in this redshift range. We present details of the data processing and the construction of the catalogs. We detected 23 of our targets in the continuum. To derive accurate infrared luminosities and obscured star formation rates, we measured the conversion factor from the ALMA 158um rest-frame dust continuum luminosity to the total infrared luminosity (LIR) after constraining the dust spectral energy distribution by stacking a photometric sample similar to ALPINE in ancillary single-dish far-infrared data. We found that our continuum detections have a median LIR of 4.4x10^11^L_{sun}_. We also detected 57 additional continuum sources in our ALMA pointings. They are at lower redshift than the ALPINE targets, with a mean photometric redshift of 2.5+/-0.2. We measured the 850um number counts between 0.35 and 3.5mJy, improving the current interferometric constraints in this flux density range. We found a slope break in the number counts around 3mJy with a shallower slope below this value. More than 40% of the cosmic infrared background is emitted by sources brighter than 0.35mJy. Finally, we detected the [CII] line in 75 of our targets. Their median [CII] luminosity is 4.8x108L_{sun}_ and their median full width at half maximum is 252km/s. After measuring the mean obscured SFR in various [CII] luminosity bins by stacking ALPINE continuum data, we find a good agreement between our data and the local and predicted SFR-L[CII] relations of De Looze et al. (2014A&A...568A..62D) and Lagache et al. (2018A&A...609A.130L).