Photon-photon and photonuclear reactions are induced by the strong electromagnetic field generated in ultra-relativistic heavy-ion collisions. These processes have been extensively studied in ultra-peripheral collisions with impact parameters larger than twice the nuclear radius. Since a few years, both the photoproduction of the $\rm J/\psi$ vector mesons and the production of dileptons via photon-photon interactions have been observed in A--A collisions with nuclear overlap. Coherent photoproduced quarkonia can probe the nuclear gluon distributions at low Bjorken-$x$, while the continuum dilepton production could be used to further map the electromagnetic fields produced in heavy-ion collisions and to study possible induced or final state effects in overlapping hadronic interactions. Both measurements are complementary to constrain the theory behind photon induced reactions in A--A collisions with nuclear overlap and the potential interaction of the measured probes with the formed and fast-expanding QGP medium. The latest ALICE results on dielectron production at low masses and pair transverse momenta at midrapidity, as well as on coherent $\rm J/\psi$ photoproduction at mid and forward rapidity, are presented for non-ultraperipheral Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ $=$ 5.02 TeV and compared with available models.