The Atacama Large Millimeter Array (ALMA) Large Program to INvestigate CII at Early times (ALPINE) targets the CII 158 μ m 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 regarding 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 (SFRs), we measured the conversion factor from the ALMA 158 μ m rest-frame dust continuum luminosity to the total infrared luminosity ( L IR ) 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 L IR of 4.4 × 10 11 L ⊙ . We also detected 57 additional continuum sources in our ALMA pointings. They are at a lower redshift than the ALPINE targets, with a mean photometric redshift of 2.5 ± 0.2. We measured the 850 μ m number counts between 0.35 and 3.5 mJy, thus improving the current interferometric constraints in this flux density range. We found a slope break in the number counts around 3 mJy with a shallower slope below this value. More than 40% of the cosmic infrared background is emitted by sources brighter than 0.35 mJy. Finally, we detected the CII line in 75 of our targets. Their median CII luminosity is 4.8 × 10 8 L ⊙ and their median full width at half maximum is 252 km s −1 . 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.