We present the results of a three-continent multisite photometric campaign carried out on the Algol-type eclipsing binary system RZ Cas, in which the primary component has recently been discovered to be a delta Sct-type pulsator. The present observations include, for the first time, complete simultaneous Strömgren uvby light curves together with a few Crawford Hbeta data collected around the orbital phase of the first quadrature. The new observations confirm the pulsational behaviour of the primary component. A detailed photometric analysis, based on these observations, is presented for both binarity and pulsation. The results indicate a semidetached system where the secondary fills its Roche lobe. The appearance of the light curves reveals the presence of the mass stream from the secondary component and a hotspot where this stream impacts on the surface of the primary star. There are also some indications of chromospheric activity in the secondary. On the other hand, the pulsational behaviour out-of-primary eclipse can be well described with only one frequency at 64.1935 cd-1 similar to the main peak found by Ohshima et al. The existence of multiperiodicity is not confirmed in our data. Concerning the mode identification, our results indicate non-radial pulsation in a high radial order (n= 6), with l= 2, |m|= 1, 2 as the most suitable. However, additional effects must be taken into account in the predictions. Moreover, the pulsation amplitude in the u band is larger than in b and v, which is unusual among the delta Sct-type variables. This can be explained as due to pulsation in a high n value and close to the blue edge of the delta Sct region. On the other hand, the early data of Ohshima et al. have also been analysed and similar results are found concerning the frequency content and pulsational amplitude. Finally, a revision of all the photometric out-of-primary-eclipse data sets available in the literature is made together with some additional unpublished data leading to interesting findings relative to changes taking place in the pulsation amplitudes and frequencies from season to season. Furthermore, multiperiodicity is probably present in some epochs.