We extend the spectral range of our stellar population synthesis models based on the MILES and CaT empirical stellar spectral libraries. For this purpose, we combine these two libraries with the Indo-U.S. to construct composite stellar spectra to feed our models. The spectral energy distributions (SEDs) computed with these models and the originally published models are combined to construct composite SEDs for single-age, single-metallicity stellar populations (SSPs) covering the range λλ3465–9469 Å at moderately high and uniform resolution (full width at half-maximum = 2.51 Å). The colours derived from these SSP SEDs provide good fits to Galactic globular cluster data. We find that the colours involving redder filters are very sensitive to the initial mass function (IMF), as well as a number of features and molecular bands throughout the spectra. To illustrate the potential use of these models, we focus on the Na i doublet at 8200 Å and with the aid of the newly synthesized SSP model SEDs, we define a new IMF-sensitive index that is based on this feature, which overcomes various limitations from previous index definitions for low-velocity dispersion stellar systems. We propose an index–index diagram based on this feature and the neighbouring Ca ii triplet at 8600 Å, to constrain the IMF if the age and [Na/Fe] abundance are known. Finally we also show a survey-oriented spectrophotometric application which evidences the accurate flux calibration of these models for carrying out reliable spectral fitting techniques. These models are available through our user-friendly website.