Thin-film solar cells based on kesterite (Cu2ZnSnSe4) material are a promising alternative for photovoltaic devices due to their composition consisting of earth abundant elements, ease of production at a relatively low temperatures and excellent optical absorption properties. Additionally, this absorber compound allows a tuneable bandgap energy in the 1 to 1.5 eV window range, which makes it an attractive candidate either as a top or a bottom solar cell in tandem technologies combined with transparent carrier-selective contacts. However, conventional kesterite devices use a toxic CdS layer as an electron-selective contact, resulting in the difficult-to-dispose chemical waste. This work explores the use of a stack of ZnO and Al-doped ZnO (AZO) films deposited by ALD to replace the CdS-based contacts in kesterite devices. The inclusion of a polyethylenimine (PEI) interlayer as dipole to enhance the overall electrical contact performance is also discussed. The transparent back contact is formed by an ALD V2Ox thin layer over a FTO conductive electrode. Fabricated kesterite solar cells exhibit remarkable photocurrent density values of 35 mAcm-2, open-circuit voltage around 260 mV and efficiencies up to 3.5% using front illumination. The aforementioned photovoltaic parameters yield to 5.3 mAcm-2, 160 mV and 0.3% respectively under back illumination, demonstrating the bifaciality of the proposed structure.