Aims. It is theoretically predicted that the Boxy/Peanut bar components have a barlens appearance (a round central component embedded in the narrow bar) at low galaxy inclinations. Here we investigate barlenses in the Calar Alto Legacy Integral Field Area (CALIFA) survey galaxies, studying their morphologies, stellar populations and metallicities. We show that, when present, barlenses account for a significant portion of light of photometric bulges (i.e. the excess light on top of the disks), which highlights the importance of bars in accumulating the central galaxy mass concentrations in the cosmic timescale. Methods. We make multi-component decompositions for a sample of 46 barlens galaxies drawn from the CALIFA survey (Sánchez, García-Benito & Zibetti 2016), with M /M = 10 9.7 -10 11.4 and z = 0.005-0.03. Unsharp masks of the Sloan Digital Sky Survey (SDSS) r'-band mosaics are used to identify the Boxy/Peanut/X features. Barlenses are identified in the images using the simulation snapshots by Salo & Laurikainen (2017) as an additional guide. Our decompositions with GALFIT include in addition to bulges, disks and bars, also barlenses as a separate component. For 26 of the decomposed galaxies the CALIFA DR2 V500 grating data-cubes are used to explore the stellar ages and metallicities, at the regions of various structure components. Results. We find that 25 ± 2% of the 1064 galaxies in the whole CALIFA sample show either X-shape or barlens feature. In the decomposed galaxies with barlenses, on average 13%±2% of the total galaxy light belongs to this component, leaving less than 10% for possible separate bulge components. Most importantly, bars and barlenses are found to have similar cumulative stellar age and metallicity distributions. The metallicities in barlenses are on average near solar, but exhibit a large range. In some of the galaxies barlenses and X-shape features appear simultaneously, in which case the bar-origin of the barlens is unambiguous. Conclusions. This is the first time that a combined morphological and stellar population analysis is used to study barlenses. We show that their stars are accumulated in a prolonged time period, concurrently with the evolution of the narrow bar.