In this work, we explore the impact of the presence of an active galactic nucleus (AGN) on the mid- and far-infrared (IR) properties of galaxies as well as the effects of simultaneous AGN and starburst activity in the same galaxies. To do this, we apply a multicomponent, multiband spectral synthesis technique to a sample of 250 μm selected galaxies of the Herschel Multi-tiered Extragalactic Survey (HerMES), with Infrared Spectrograph (IRS) spectra available for all galaxies. Our results confirm that the inclusion of the IRS spectra plays a crucial role in the spectral analysis of galaxies with an AGN component improving the selection of the best-fitting hot dust (torus) model. We find a correlation between the obscured star formation rate, SFRIR, derived from the IR luminosity of the starburst component, and SFRPAH, derived from the luminosity of the PAH features, L PAH, with SFRFIR taking higher values than SFRPAH. The correlation is different for AGN- and starburst-dominated objects. The ratio of L PAH to that of the starburst component, L PAH/L SB, is almost constant for AGN-dominated objects but decreases with increasing L SB for starburst-dominated objects. SFRFIR increases with the accretion luminosity, L acc, with the increase less prominent for the very brightest, unobscured AGN-dominated sources. We find no correlation between the masses of the hot (AGN-heated) and cold (starburst-heated) dust components. We interpret this as a non-constant fraction of gas driven by the gravitational effects to the AGN while the starburst is ongoing. We also find no evidence of the AGN affecting the temperature of the cold dust component, though this conclusion is mostly based on objects with a non-dominant AGN component. We conclude that our findings do not provide evidence that the presence of AGN affects the star formation process in the host galaxy, but rather that the two phenomena occur simultaneously over a wide range of luminosities.