We present Atacama Large Millimeter/Submillimeter Array (ALMA) continuum observations of a sample of nine star-forming galaxies at redshifts 1.47 and 2.23 selected from the High-z Emission Line Survey (HiZELS). Four galaxies in our sample are detected at high significance by ALMA at a resolution of 0${_{.}^{\prime\prime}}$25 at rest-frame 355 μm. Together with the previously observed Hα emission, from adaptive optics-assisted integral-field-unit spectroscopy (∼0${_{.}^{\prime\prime}}$15 resolution), and F606W and F140W imaging from the Hubble Space Telescope (∼0${_{.}^{\prime\prime}}$2 resolution), we study the star-formation activity, stellar and dust mass in these high-redshift galaxies at ∼kpc-scale resolution. We find that ALMA detection rates are higher for more massive galaxies (M* > 1010.5 M⊙) and higher [N ii]/Hα ratios (>0.25, a proxy for gas-phase metallicity). The dust extends out to a radius of 8 kpc, with a smooth structure, even for those galaxies presenting clumpy Hα morphologies. The half-light radii (Rdust) derived for the detected galaxies are of the order ∼4.5 kpc, more than twice the size of submillimetre-selected galaxies at a similar redshift. Our global star-formation rate estimates — from far-IR and extinction-corrected Hα luminosities — are in good agreement. However, the different morphologies of the different phases of the interstellar medium suggest complex extinction properties of the high-redshift normal galaxies.