Context. The general properties (e.g., activity class, star formation rates, metallicities, extinctions, average ages, etc.) of luminous (LIRGs) and ultraluminous infrared galaxies (ULIRGs) in the local universe are well known because large samples of these objects have been the subject of numerous spectroscopic works over the past three decades. There are, however, relatively few studies of the spatially-resolved spectroscopic properties of large samples of LIRGs and ULIRGs using integral field spectroscopy (IFS). Aims: We are carrying out an IFS survey of local (z<0.26) samples of LIRGs and ULIRGs to characterize their two-dimensional spectroscopic properties. The main goal of this paper is to study the spatially resolved properties of the stellar populations and the excitation conditions in a sample of LIRGs. Methods: We analyze optical (3800-7200 Å) IFS data taken with the Potsdam Multi-Aperture Spectrophotometer (PMAS) of the central few kiloparsecs of eleven LIRGs. To study these stellar populations, we fit the optical stellar continuum and the hydrogen recombination lines of selected regions in the galaxies. We analyzed the excitation conditions of the gas using the spatially resolved properties of the brightest optical emission lines. We complemented the PMAS observations with existing HST/NICMOS near-infrared continuum and Paα imaging. Results: The optical continua of selected regions in our LIRGs are well fitted with a combination of an evolved (~0.7-10 Gyr) stellar population with an ionizing stellar population (1-20 Myr). The latter population is more obscured than the evolved population, and has visual extinctions in good agreement with those obtained from the Balmer decrement. Except for NGC 7771, we find no clear that there is an important contribution to the optical light from an intermediate-aged stellar population (~100-500 Myr). Even after correcting for the presence of stellar absorption, a large number of spaxels with low observed equivalent widths of Hα in emission still show enhanced [N ii]λ6584/Hα and [S ii]λλ6717, 6731/Hα ratios. These ratios are likely to be produced by a combination of photoionization in H ii regions and diffuse emission. These regions of enhanced line ratios are generally coincident with low surface-brightness H ii regions and diffuse emission detected in the Hα and Paα images. We used the PMAS spatially resolved line ratios and the NICMOS Paα photometry of H ii regions to derive the fraction of diffuse emission in LIRGs. We find that this fraction varies from galaxy to galaxy, and it is generally less than 60%, as found in other starburst galaxies. Based on observations collected at the German-Spanish Astronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut für Astronomie Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC).Figures 1b-1j and 2b-2j are only available in electronic form at http://www.aanda.org