We present the results on broadband X-ray properties of persistent black hole binaries GRS 1758−258 and 1E 1740.7−2942 using AstroSat, NuSTAR and Swift-XRT observations carried out during 2016−2022. We perform spectral modeling of both sources after eliminating the contamination in their LAXPC spectra from nearby X-ray sources. Preliminary spectral modelling using Comptonization and line emission (∼ 6.4 keV) models suggest that GRS 1758−258 occupies both dim-soft state (kTbb = 0.37 ± 0.01 keV, Γ ∼ 5.9, $L_{bol}=1\%$ of Eddington luminosity LEdd) and hard state (Γ = 1.64 − 2.22, kTe=4−45 keV, Lbol=1−5% LEdd) that requires a multi-colour disc blackbody model (kTin = 0.54 ± 0.01 keV) occasionally. 1E 1740.7−2942 instead is found only in hard state (Γ=1.67−2.32, kTe=5−16 keV, Lbol=1−2% LEdd). Reflection properties of both sources are studied by applying relativistic reflection model RELXILL to the broadband spectra. Our results from AstroSat and NuSTAR consistently unveiled the presence of a Comptonizing region along with an ionized reflection region (ionization parameter logξ=2.7−3.8 and 2.7−4.7 erg cm s−1 in GRS 1758−258 and 1E 1740.7−2942 respectively) in both sources. Reflection modeling revealed GRS 1758−258 to have a high metal abundance ($A_{fe}=3.9^{+0.4}_{-0.3}$ times solar metal abundance) and inclination angle (i) of 61 ± 2○. In case of 1E 1740.7−2942, i is constrained to be 55 ± 1○. Finally, we discuss the implication of our findings in the context of accretion dynamics by comparing our results with the previous studies.