Star-forming clumps have been found to significantly influence the star formation of gas-rich z > 1 galaxies. Using public data from JWST/NIRCam (Cosmic Evolution Survey; COSMOS-Web) and Atacama Large (sub-)Millimeter Array (ALMA; Fiber-Multi Object Spectrograph or FMOS-COSMOS survey), we study a sample of 32 massive (>10(10.5)M(circle dot)) main-sequence galaxies at z(spec)similar to 1.5 with similar to 0.3kpc resolution. We create composite morphological models consisting of bulge, disc, and clumps to fully 'deconstruct' the galaxy images. With the resulting measurements of the flux and size of these components, we find the following: (i) the combined contribution of clumps is 1-30 per cent towards the net star formation of the host while contributing 1-20 per cent to its stellar mass. The clumps show a correlation between their stellar mass and star formation rate (SFR), but have an increased specific SFR relative to the star formation main-sequence, with offsets ranging from 0 less than or similar to Delta log sSFR less than or similar to 0.4. They feature star formation surface densities of 10(-2)-10(2)M(circle dot)yr(-1)kpc(-2), consistent with values observed in both local star-forming and starburst galaxies. (ii) The detected clumps span a large range of characteristic sizes (r(e) similar to 0.1-1kpc) and stellar masses (similar to 10(8.0-9.5)M(circle dot)). We estimate a mass-size relation (r(e) proportional to M-star(0.52 +/- 0.07)) along with a stellar mass function (slope, alpha= -1.85 +/- 0.19), both suggesting a hierarchical nature similar to that expected in star-forming regions in local galaxies. (iii) Our measurements agree with the properties of stellar clumps in z greater than or similar to 1 lensed systems, bridging the gap between lensed and unlensed studies by detecting structures at sub-kpc scales. (iv) Clumps are found to be preferentially located along spiral features visible primarily in the residual rest frame near-IR images. In conclusion, we present an observation-based, coherent picture of star-forming clumps in galaxies at z > 1.