Aims. This work explores, from a statistical point of view, the rest-frame far-ultraviolet (FUV) to far-infrared (FIR) emission of a population of Lyman-break galaxies (LBGs) at z ∼ 3 that cannot be individually detected from current FIR observations. Methods. We performed a stacking analysis over a sample of ∼17 000 LBGs at redshift 2.5 < z < 3.5 in the COSMOS field. The sample is binned as a function of UV luminosity (L_FUV), UV continuum slope (β_UV), and stellar mass (M_*), and then stacked at optical (BVriz bands), near-infrared (YJHK_s bands), IRAC (3.6, 4.5, 5.6, and 8.0 μm), MIPS (24 μm), PACS (100 and 160 μm), SPIRE (250, 350, and 500 μm), and AzTEC (1.1 mm) observations. We obtained 30 rest-frame FUV-to-FIR spectral energy distributions (SEDs) of LBGs at z ∼ 3, and analyzed these with the CIGALE SED-fitting analysis code. We were able to derive fully consistent physical parameters, that is, M_*, β_UV, L_FUV, L_IR, A_FUV, star formation rate, and the slope of the dust attenuation law; we built a semiempirical library of 30 rest-frame FUV-to-FIR stacked LBG SEDs as functions of L_FUV, β_UV, and M_*. Results. We used the so-called IR-excess (IRX ≡ L_IR/L_FUV) to investigate the dust attenuation as a function of β_UV and M_*. Our LBGs, averaged as a function of β_UV, follow the well-known IRX–β_UV calibration of local starburst galaxies. Stacks as a function of M_* follow the IRX–M_* relationship presented in the literature at high M_* (log(M_* [M_⊙]) > 10). However, a large dispersion is shown in the IRX–β_UV and IRX–M_* planes, in which the β_UV and M_* are combined to average the sample. Additionally, the SED-fitting analysis results provide a diversity of dust attenuation curve along the LBG sample, and their slopes are well correlated with M_*. Steeper dust attenuation curves than Calzetti’s are favored in low stellar mass LBGs (log(M_* [M_⊙]) < 10.25), while grayer dust attenuation curves are favored in high stellar mass LBGs (log(M_* [M_⊙]) > 10.25). We also demonstrate that the slope of the dust attenuation curves is one of the main drivers that shapes the IRX–β_UV plane.